Bibliographies thématiques / Numerical analysis of partial differential equation

Littérature scientifique sur le sujet « Numerical analysis of partial differential equation »

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Publié le 13 juillet 2024

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Articles de revues sur le sujet "Numerical analysis of partial differential equation"

Alharthi, Nadiyah Hussain, Abdon Atangana et Badr S. Alkahtani. « Numerical analysis of some partial differential equations with fractal-fractional derivative ». AIMS Mathematics 8, n^o 1 (2022) : 2240–56. http://dx.doi.org/10.3934/math.2023116.

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<abstract> <p>In this study, we expanded the partial differential equation framework to which fractal-fractional differentiation can be applied. For this, we employed the generalized Mittag-Leffler function, and the fractal-fractional derivatives based on the power-law kernel. A general partial differential equation with the fractal-fractional derivative, the power law kernel and the generalized Mittag-Leffler function was thoroughly examined. There is almost no numerical scheme for solving partial differential equations with fractal-fractional derivatives, as less investigation has been done in this direction in the last decades. In this work, therefore, we shall attempt to provide a numerical method that might be used to solve these equations in each circumstance. The heat equation was taken into consideration for the application and numerically solved using a few simulations for various values of fractional and fractal orders. It is observed that, when the fractal order is 1, one obtains fractional partial differential equations which have been known to replicate nonlocal behaviors. Meanwhile, if the fractional order is 1, one obtains fractal-partial differential equations. Thus, when the fractional order and fractal dimension are different from zero, nonlocal processes with similar features are developed.</p> </abstract>

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Kurbonov, Elyorjon, Nodir Rakhimov, Shokhabbos Juraev et Feruza Islamova. « Derive the finite difference scheme for the numerical solution of the first-order diffusion equation IBVP using the Crank-Nicolson method ». E3S Web of Conferences 402 (2023) : 03029. http://dx.doi.org/10.1051/e3sconf/202340203029.

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In the article, a differential scheme is created for the the first-order diffusion equation using the Crank-Nicolson method. The stability of the differential scheme was checked using the Neumann method. To solve the problem numerically, stability intervals were found using the Neman method. This work presents an analysis of the stability of the Crank-Nicolson scheme for the two-dimensional diffusion equation using Von Neumann stability analysis. The Crank-Nicolson scheme is a widely used numerical method for solving partial differential equations that combines the explicit and implicit schemes. The stability analysis is an important factor to consider when choosing a numerical method for solving partial differential equations, as numerical instability can cause inaccurate solutions. We show that the Crank-Nicolson scheme is unconditionally stable, meaning that it can be used for a wide range of parameters without being affected by numerical instability. Overall, the analysis and implementation presented in this work provide a framework for designing and analyzing numerical methods for solving partial differential equations using the Crank-Nicolson scheme. The stability analysis is crucial for ensuring the accuracy and reliability of numerical solutions of partial differential equations.

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Sanz-Serna, J. M. « A Numerical Method for a Partial Integro-Differential Equation ». SIAM Journal on Numerical Analysis 25, n^o 2 (avril 1988) : 319–27. http://dx.doi.org/10.1137/0725022.

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Zhao, J., M. S. Cheung et S. F. Ng. « Spline Kantorovich method and analysis of general slab bridge deck ». Canadian Journal of Civil Engineering 25, n^o 5 (1 octobre 1998) : 935–42. http://dx.doi.org/10.1139/l98-030.

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In this paper, the spline Kantorovich method is developed and applied to the analysis and design of bridge decks. First, the bridge deck is mapped into a unit square in the Xi - eta plane. The governing partial differential equation of the plate is reduced to the ordinary differential equation in the longitudinal direction of the bridge by the routine Kantorovich method. Spline point collocation method is then used to solve the derived ordinary differential equation to obtain the displacements and internal forces of the bridge deck. Mindlin plate theory is incorporated into the differential equation and, as a result, the effect of shear deformation of the plate is also considered. Possible shear locking is avoided by the reduced integration technique. Numerical examples show that the proposed new numerical model is versatile, efficient, and reliable.Key words: Kantorovich method, spline function, partial differential equations, ordinary differential equations, point collocation method, bridge deck.

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Pyanylo, Yaroslav, et Galyna Pyanylo. « Analysis of approaches to mass-transfer modeling n non-stationary mode ». Physico-mathematical modelling and informational technologies, n^o 28, 29 (27 décembre 2019) : 55–64. http://dx.doi.org/10.15407/fmmit2020.28.055.

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A significant number of natural and physical processes are described by differential equations in partial derivatives or systems of differential equations in partial derivatives. Numerical methods have been found to find their solutions. Partial derivatives systems are solved mainly by reducing the order of the system of equations or reducing it to one differential equation. This procedure leads to an increase in the order of the differential equation. There are various restrictions and errors that can lead to additional solutions, boundary conditions for intermediate derivatives, and so on. The work is devoted to the analysis of such situations and ways of exit.

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Abrashina-Zhadaeva, N., et N. Romanova. « Vector Additive Decomposition for 2D Fractional Diffusion Equation ». Nonlinear Analysis : Modelling and Control 13, n^o 2 (25 avril 2008) : 137–43. http://dx.doi.org/10.15388/na.2008.13.2.14574.

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Such physical processes as the diffusion in the environments with fractal geometry and the particles’ subdiffusion lead to the initial value problems for the nonlocal fractional order partial differential equations. These equations are the generalization of the classical integer order differential equations. An analytical solution for fractional order differential equation with the constant coefficients is obtained in [1] by using Laplace-Fourier transform. However, nowadays many of the practical problems are described by the models with variable coefficients. In this paper we discuss the numerical vector decomposition model which is based on a shifted version of usual Gr¨unwald finite-difference approximation [2] for the non-local fractional order operators. We prove the unconditional stability of the method for the fractional diffusion equation with Dirichlet boundary conditions. Moreover, a numerical example using a finite difference algorithm for 2D fractional order partial differential equations is also presented and compared with the exact analytical solution.

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Reinfelds, Andrejs, Olgerts Dumbrajs, Harijs Kalis, Janis Cepitis et Dana Constantinescu. « NUMERICAL EXPERIMENTS WITH SINGLE MODE GYROTRON EQUATIONS ». Mathematical Modelling and Analysis 17, n^o 2 (1 avril 2012) : 251–70. http://dx.doi.org/10.3846/13926292.2012.662659.

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Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary problems in large time interval with complex oscillating initial conditions. We use the implicit finite difference schemes and the method of lines realized with MATLAB. Two versions of gyrotron equation are investigated. We consider different methods for modelling new and old versions of the gyrotron equations. The main physical result is the possibility to determine the maximal value of the wave amplitude and the electron efficiency coefficient.

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Company, R., L. Jódar, M. Fakharany et M. C. Casabán. « Removing the Correlation Term in Option Pricing Heston Model : Numerical Analysis and Computing ». Abstract and Applied Analysis 2013 (2013) : 1–11. http://dx.doi.org/10.1155/2013/246724.

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This paper deals with the numerical solution of option pricing stochastic volatility model described by a time-dependent, two-dimensional convection-diffusion reaction equation. Firstly, the mixed spatial derivative of the partial differential equation (PDE) is removed by means of the classical technique for reduction of second-order linear partial differential equations to canonical form. An explicit difference scheme with positive coefficients and only five-point computational stencil is constructed. The boundary conditions are adapted to the boundaries of the rhomboid transformed numerical domain. Consistency of the scheme with the PDE is shown and stepsize discretization conditions in order to guarantee stability are established. Illustrative numerical examples are included.

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Kim, Sung-Hoon, et Youn-sik Park. « An Improved Finite Difference Type Numerical Method for Structural Dynamic Analysis ». Shock and Vibration 1, n^o 6 (1994) : 569–83. http://dx.doi.org/10.1155/1994/139352.

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An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.

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Ratas, Mart, Andrus Salupere et Jüri Majak. « SOLVING NONLINEAR PDES USING THE HIGHER ORDER HAAR WAVELET METHOD ON NONUNIFORM AND ADAPTIVE GRIDS ». Mathematical Modelling and Analysis 26, n^o 1 (18 janvier 2021) : 147–69. http://dx.doi.org/10.3846/mma.2021.12920.

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The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon equation are used as model equations. Adaptive as well as nonadaptive nonuniform grids are developed and used to solve the model equations numerically. The numerical results are compared to the known analytical solutions as well as to the numerical solutions obtained by application of the HOHWM on a uniform grid. The proposed methods of using nonuniform grid are shown to significantly increase the accuracy of the HOHWM at the same number of grid points.

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Thèses sur le sujet "Numerical analysis of partial differential equation"

Cinar, Selahittin. « Analysis of a Partial Differential Equation Model of Surface Electromigration ». TopSCHOLAR®, 2014. https://digitalcommons.wku.edu/theses/1368.

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A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.

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Sundqvist, Per. « Numerical Computations with Fundamental Solutions ». Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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Ozmen, Neslihan. « Image Segmentation And Smoothing Via Partial Differential Equations ». Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610395/index.pdf.

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In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical imagery, object tracking etc. The model is a way of finding a partition of an image by using a piecewise smooth representation of the image. Unfortunately numerical procedures for minimizing the Mumford-Shah functional have some difficulties because the problem is non convex and it has numerous local minima, so approximate approaches have been proposed. Two such methods are the Ambrosio-Tortorelli approximation and the Chan-Vese active contour method. Ambrosio and Tortorelli have developed a practical numerical implementation of the Mumford-Shah model which based on an elliptic approximation of the original functional. The Chan-Vese model is a piecewise constant generalization of the Mumford-Shah functional and it is based on level set formulation. Another widely used image segmentation technique is the &ldquo
Active Contours (Snakes)&rdquo
model and it is correlated with the Chan-Vese model. In this study, all these approaches have been examined in detail. Mathematical and numerical analysis of these models are studied and some experiments are performed to compare their performance.

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Kwok, Ting On. « Adaptive meshless methods for solving partial differential equations ». HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1076.

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Pietschmann, Jan-Frederik. « On some partial differential equation models in socio-economic contexts : analysis and numerical simulations ». Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/241495.

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This thesis deals with the analysis and numerical simulation of different partial differential equation models arising in socioeconomic sciences. It is divided into two parts: The first part deals with a mean-field price formation model introduced by Lasry andLions in 2007. This model describes the dynamic behaviour of the price of a good being traded between a group of buyers and a group of vendors. Existence (locally in time) of smooth solutions is established, and obstructions to proving a global existence result are examined. Also, properties of a regularised version of the model are explored and numerical examples are shown. Furthermore, the possibility of reconstructing the initial datum given a number of observations, regarding the price and the transaction rate, is considered. Using a variational approach, the problem can be expressed as a non-linear constrained minimization problem. We show that the initial datum is uniquely determined by the price (identifiability). Furthermore, a numerical scheme is implemented and a variety of examples are presented. The second part of this thesis treats two different models describing the motion of (large) human crowds. For the first model, introduced by R.L. Hughes in 2002, several regularised versions are considered. Existence and uniqueness of entropy solutions are proven using the technique of vanishing viscosity. In one space dimension, the dynamic behaviour of solutions of the original model is explored for some special cases. These results are compared to numerical simulations. Moreover, we consider a discrete cellular automaton model introduced by A. Kirchner and A. Schadschneider in 2002.By (formally) passing to the continuum limit, we obtain a system of partial differential equations. Some analytical properties, such as linear stability of stationary states, areexamined and extensive numerical simulations show capabilities and limitations of the model in both the discrete and continuous setting.

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von, Schwerin Erik. « Convergence rates of adaptive algorithms for stochastic and partial differential equations ». Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302.

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Zhang, Wei. « Local absorbing boundary conditions for Korteweg-de-Vries-type equations ». HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/83.

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The physicists and mathematicians have put a lot of eﬀorts in the numerical analysis of various types of partial diﬀerential equations on unbounded domain. The time- dependent partial diﬀerential equations(PDEs) also have a wide range of applications in physics, geography and many other interdisciplines. This thesis is concerned with the numerical solutions of such kind of partial diﬀerential equations on unbounded spatial domain, especially the Korteweg-de Vries(KdV) equations. Since it is unable to solve the problem directly due to its unboundedness, the common way to surpass such diﬃculty is to introduce proper conditions on the truncated artiﬁcial boundaries and to approximate the problem on a bounded domain, which is also known as the Absorbing Boundary Conditions(ABCs). One of the main contributions of this thesis is to design accurate local absorbing boundary conditions for linearized KdV equations and to extend the method to non- linear KdV equations on unbounded domain. Pad´e approximation is the main tool to approximate the cubic root in the construction of local absorbing boundary conditions(LABCs) for a linearized KdV equation on unbounded domain. Besides, we also introduce the continued fraction method in the approximation of cubic root. To avoid the high-order derivatives in the absorbing boundary conditions, a sequence of auxiliary variables are applied accordingly. Then the original problem on unbounded domain is reduced to an approximated initial boundary value(IBV) problem deﬁned on a ﬁnite domain. Based on previous work, we are able to extend the method to the design of eﬃcient local absorbing boundary conditions for nonlinear KdV equations on unbounded domain. The unifying approach method is applied to this nonlinear case. The idea of the unifying approach method is to separate inward- and outward-going waves and to build suitable approximated linear operator with a “one-way operator”. Then we unite the approximated linear operator with the nonlinear subproblem and propose boundary conditions for the nonlinear subproblem along the artiﬁcial boundaries. The numerical simulations are given to demonstrate the eﬀectiveness and accuracy of our local absorbing boundary conditions. Keywords: Korteweg-de Vries equation; Local absorbing boundary conditions; Pad´e approximation; Continued fraction method; Unifying approach.

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Carlsson, Jesper. « Optimal Control of Partial Differential Equations in Optimal Design ». Doctoral thesis, KTH, Numerisk Analys och Datalogi, NADA, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9293.

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This thesis concerns the approximation of optimally controlled partial differential equations for inverse problems in optimal design. Important examples of such problems are optimal material design and parameter reconstruction. In optimal material design the goal is to construct a material that meets some optimality criterion, e.g. to design a beam, with fixed weight, that is as stiff as possible. Parameter reconstrucion concerns, for example, the problem to find the interior structure of a material from surface displacement measurements resulting from applied external forces. Optimal control problems, particularly for partial differential equations, are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its Hamiltonian system is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L² projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. Another treated issue is the relevance of input data for parameter reconstruction problems, where the goal is to determine a spacially distributed coefficient of a partial differential equation from partial observations of the solution. It is here shown that the choice of input data, that generates the partial observations, affects the reconstruction, and that it is possible to formulate meaningful optimality criteria for the input data that enhances the quality of the reconstructed coefficient. In the thesis we present solutions to various applications in optimal material design and reconstruction.
Denna avhandling handlar om approximation av optimalt styrda partiella differentialekvationer för inversa problem inom optimal design. Viktiga exempel på sådana problem är optimal materialdesign och parameterskattning. Inom materialdesign är målet att konstruera ett material som uppfyller vissa optimalitetsvillkor, t.ex. att konstruera en så styv balk som möjligt under en given vikt, medan ett exempel på parameterskattning är att hitta den inre strukturen hos ett material genom att applicera ytkrafter och mäta de resulterande förskjutningarna. Problem inom optimal styrning, speciellt för styrning av partiella differentialekvationer,är ofta illa ställa och måste regulariseras för att kunna lösas numeriskt. Teorin för Hamilton-Jacobi-Bellmans ekvationer används här för att konstruera regulariseringar och ge feluppskattningar till problem inom optimaldesign. Den konstruerade Pontryaginmetoden är en enkel och generell metod där det första analytiska steget är att regularisera Hamiltonianen. I nästa steg löses det Hamiltonska systemet effektivt med Newtons metod och en gles Jacobian. Vi härleder även en feluppskattning för skillnaden mellan den exakta och den approximerade målfunktionen. Denna uppskattning beror endast på skillnaden mellan den sanna och den regulariserade, ändligt dimensionella, Hamiltonianen, båda utvärderade längst lösningsbanan och dessL²-projektion. Felet beror alltså ej på skillnaden mellan den exakta och denapproximativa lösningen till det Hamiltonska systemet. Ett annat fall som behandlas är frågan hur indata ska väljas för parameterskattningsproblem. För sådana problem är målet vanligen att bestämma en rumsligt beroende koefficient till en partiell differentialekvation, givet ofullständiga mätningar av lösningen. Här visas att valet av indata, som genererarde ofullständiga mätningarna, påverkar parameterskattningen, och att det är möjligt att formulera meningsfulla optimalitetsvillkor för indata som ökar kvaliteten på parameterskattningen. I avhandlingen presenteras lösningar för diverse tillämpningar inom optimal materialdesign och parameterskattning.
QC 20100712

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Le, Gia Quoc Thong. « Approximation of linear partial differential equations on spheres ». Texas A&M University, 2003. http://hdl.handle.net/1969.1/22.

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The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both the finite element method and the collocation method are discussed. In the heat equation, only the collocation method is considered. Error estimates in the supremum norms and the Sobolev norms are obtained when certain regularity conditions are imposed on the spherical basis functions.

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Cheung, Ka Chun. « Meshless algorithm for partial differential equations on open and singular surfaces ». HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/278.

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Radial Basis function (RBF) method for solving partial differential equation (PDE) has a lot of applications in many areas. One of the advantages of RBF method is meshless. The cost of mesh generation can be reduced by playing with scattered data. It can also allow adaptivity to solve some problems with special feature. In this thesis, RBF method will be considered to solve several problems. Firstly, we solve the PDEs on surface with singularity (folded surface) by a localized method. The localized method is a generalization of finite difference method. A priori error estimate for the discreitzation of Laplace operator is given for points selection. A stable solver (RBF-QR) is used to avoid ill-conditioning for the numerical simulation. Secondly, a {dollar}H^2{dollar} convergence study for the least-squares kernel collocation method, a.k.a. least-square Kansa's method will be discussed. This chapter can be separated into two main parts: constraint least-square method and weighted least-square method. For both methods, stability and consistency analysis are considered. Error estimate for both methods are also provided. For the case of weighted least-square Kansa's method, we figured out a suitable weighting for optimal error estimation. In Chapter two, we solve partial differential equation on smooth surface by an embedding method in the embedding space {dollar}\R^d{dollar}. Therefore, one can apply any numerical method in {dollar}\R^d{dollar} to solve the embedding problem. Thus, as an application of previous result, we solve embedding problem by least-squares kernel collocation. Moreover, we propose a new embedding condition in this chapter which has high order of convergence. As a result, we solve partial differential equation on smooth surface with a high order kernel collocation method. Similar to chapter two, we also provide error estimate for the numerical solution. Some applications such as pattern formation in the Brusselator system and excitable media in FitzHughNagumo model are also studied.

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Livres sur le sujet "Numerical analysis of partial differential equation"

Lui, S. H. Numerical analysis of partial differential equations. Hoboken, N.J : Wiley, 2011.

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Lui, S. H. Numerical Analysis of Partial Differential Equations. Hoboken, NJ, USA : John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118111130.

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Lions, Jacques Louis, dir. Numerical Analysis of Partial Differential Equations. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11057-3.

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Lui, S. H. Numerical analysis of partial differential equations. Hoboken, N.J : Wiley, 2011.

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A, Hall Charles. Numerical analysis of partial differential equations. Englewood Cliffs, N.J : Prentice Hall, 1990.

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Lions, J. L. Numerical Analysis of Partial Differential Equations. Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011.

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Evans, Gwynne A. Analytic Methods for Partial Differential Equations. London : Springer London, 1999.

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Mattheij, Robert M. M. Partial differential equations : Modeling, analysis, computation. Philadelphia : Society for Industrial and Applied Mathematics, 2005.

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Grossman, Christian. Numerical treatment of partial differential equations. Germany [1990-onward] : Springer Verlag, 2007.

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Evans, Gwynne. Numerical methods for partial differential equations. London : Springer, 2000.

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Chapitres de livres sur le sujet "Numerical analysis of partial differential equation"

Madenci, Erdogan, Atila Barut et Mehmet Dorduncu. « Partial Differential Equations ». Dans Peridynamic Differential Operator for Numerical Analysis, 117–57. Cham : Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02647-9_6.

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Maury, Bertrand. « Numerical Analysis of a Finite Element/Volume Penalty Method ». Dans Partial Differential Equations, 167–85. Dordrecht : Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_9.

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Bredies, Kristian, et Dirk Lorenz. « Partial Differential Equations in Image Processing ». Dans Applied and Numerical Harmonic Analysis, 171–250. Cham : Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01458-2_5.

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Saha Ray, Santanu. « Numerical Solutions of Partial Differential Equations ». Dans Numerical Analysis with Algorithms and Programming, 591–640. Boca Raton : Taylor & Francis, 2016. | “A CRC title.” : Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315369174-10.

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Fox, William P., et Richard D. West. « Numerical Solutions to Partial Differential Equations ». Dans Numerical Methods and Analysis with Mathematical Modelling, 362–81. Boca Raton : Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781032703671-13.

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Casas, Eduardo, et Mariano Mateos. « Optimal Control of Partial Differential Equations ». Dans Computational Mathematics, Numerical Analysis and Applications, 3–59. Cham : Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49631-3_1.

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Capriz, G. « The Numerical Approach to Hydrodynamic Problems ». Dans Numerical Analysis of Partial Differential Equations, 109–59. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11057-3_4.

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Verdi, Claudio. « Stefan Problems and Numerical Analysis ». Dans Analysis and Numerics of Partial Differential Equations, 37–45. Milano : Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2592-9_5.

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Lasota, A. « Contintent Equations and Boundary Value Problems ». Dans Numerical Analysis of Partial Differential Equations, 255–66. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11057-3_10.

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Albertoni, S. « Alcuni Metodi di Calcolo Nella Teoria della Diffusione dei Neutroni ». Dans Numerical Analysis of Partial Differential Equations, 2–23. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11057-3_1.

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Actes de conférences sur le sujet "Numerical analysis of partial differential equation"

Hong, Jialin, et Xiuling Yin. « The well-posedness of a special partial differential equation ». Dans NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012 : International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756518.

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Francomano, Elisa, Adele Tortorici, Elena Toscano, Guido Ala, Theodore E. Simos, George Psihoyios et Ch Tsitouras. « Multiscale Particle Method in Solving Partial Differential Equations ». Dans Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790115.

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Nečasová, Gabriela, et Václav Šátek. « Parallel solution of parabolic partial differential equation using higher-order method ». Dans INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS : ICNAAM2022. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0212373.

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Casas, Eduardo, Theodore E. Simos, George Psihoyios et Ch Tsitouras. « Symposium on Optimal Control of Partial Differential Equations ». Dans NUMERICAL ANALYSIS AND APPLIED MATHEMATICS : International Conference on Numerical Analysis and Applied Mathematics 2009 : Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241320.

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Sandu, Adrian, Emil M. Constantinescu, Theodore E. Simos, George Psihoyios et Ch Tsitouras. « Multirate Time Discretizations for Hyperbolic Partial Differential Equations ». Dans NUMERICAL ANALYSIS AND APPLIED MATHEMATICS : International Conference on Numerical Analysis and Applied Mathematics 2009 : Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241354.

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Ashyralyev, Allaberen, et Kheireddine Belakroum. « Numerical study of nonlocal BVP for a third order partial differential equation ». Dans INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040592.

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Zhang, Wei, et Shufeng Lu. « Nonlinear Numerical Analysis of Extruding Cantilever Laminated Composite Plates ». Dans ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70252.

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This paper focus on the nonlinear numerical analysis for an extruding cantilever laminated composite plates subjected to transversal and in-plane excitation. Based on the Reddy’s shear deformable plate theory, the nonlinear partial differential equations of motion were established by using the Hamilton Principal. And then, after choosing suitable vibration mode-shape functions, the Galerkin method was used to reduce the governing partial differential equations to a two-degree-of-freedom nonlinear ordinary differential equation. Finally, we numerical solved the nonlinear ordinary differential equation, and analyzed the influences of varying extruding speeds and thickness of plates on the stability of the plates.

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Ashyralyev, Allaberen, Kheireddine Belakroum et Assia Guezane-Lakoud. « Numerical algorithm for the third-order partial differential equation with local boundary conditions ». Dans INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000624.

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Ashyralyev, Allaberen, Kheireddine Belakroum et Assia Guezane-Lakoud. « Numerical algorithm for the third-order partial differential equation with nonlocal boundary conditions ». Dans INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000628.

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Miyatake, Yuto, et Takayasu Matsuo. « Energy conservative/dissipative H1-Galerkin semi-discretizations for partial differential equations ». Dans NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012 : International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756385.

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Rapports d'organisations sur le sujet "Numerical analysis of partial differential equation"

Dahlgren, Kathryn Marie, Francesco Rizzi, Karla Vanessa Morris et Bert Debusschere. Rexsss Performance Analysis : Domain Decomposition Algorithm Implementations for Resilient Numerical Partial Differential Equation Solvers. Office of Scientific and Technical Information (OSTI), août 2014. http://dx.doi.org/10.2172/1171553.

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French, Donald A. Numerical Analysis and Computation of Nonlinear Partial Differential Equations from Applied Mathematics. Fort Belvoir, VA : Defense Technical Information Center, novembre 1993. http://dx.doi.org/10.21236/ada275582.

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French, Donald A. Numerical Analysis and Computation of Nonlinear Partial Differential Equations from Applied Mathematics. Fort Belvoir, VA : Defense Technical Information Center, octobre 1990. http://dx.doi.org/10.21236/ada231188.

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Sparks, Paul, Jesse Sherburn, William Heard et Brett Williams. Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods. Engineer Research and Development Center (U.S.), septembre 2021. http://dx.doi.org/10.21079/11681/41963.

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Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it runs inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. Results of numerical investigations will be compared with results of penetration experiments.

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Glover, Joseph, et Kai L. Chung. Probablistic Analysis of Semilinear Partial Differential Equation. Fort Belvoir, VA : Defense Technical Information Center, octobre 1986. http://dx.doi.org/10.21236/ada177314.

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Michalopoulos, C. D. PR-175-420-R01 Submarine Pipeline Analysis - Theoretical Manual. Chantilly, Virginia : Pipeline Research Council International, Inc. (PRCI), décembre 1985. http://dx.doi.org/10.55274/r0012171.

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Describes the computer program SPAN which computes the nonlinear transient response of a submarine pipeline, in contact with the ocean floor, to wave and current excitation. The dynamic response of a pipeline to impact loads, such as loads from trawl gear of fishing vessels, may also be computed. In addition, thermal expansion problems for submarine pipelines may be solved using SPAN. Beam finite element theory is used for spatial discretization of the partial differential equations governing the motion of a submarine pipeline. Large-deflection, small-strain theory is employed. The formulation involves a consistent basis and added mass matrix. Quadratic drag is computed using a nonconventional approach that involves the beam shape functions. Soil-resistance loads are computed using unique pipeline-soil interaction models which take into account coupling of axial and lateral soil forces. The nonlinear governing equations are solved numerically using the Newmark Method. This manual presents the discretized equations of motion, the methods used in determining hydrodynamic and soil-resistance forces, and the solution method.

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