Relevant bibliographies by topics / Differential Equation Method de Wormald

Academic literature on the topic 'Differential Equation Method de Wormald'

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Published: 25 May 2024

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Journal articles on the topic "Differential Equation Method de Wormald"

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Zou, Li, Zhen Wang, and Zhi Zong. "Generalized differential transform method to differential-difference equation." Physics Letters A 373, no. 45 (November 2009): 4142–51. http://dx.doi.org/10.1016/j.physleta.2009.09.036.

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Li, Meng-Rong, Tzong-Hann Shieh, C. Jack Yue, Pin Lee, and Yu-Tso Li. "Parabola Method in Ordinary Differential Equation." Taiwanese Journal of Mathematics 15, no. 4 (August 2011): 1841–57. http://dx.doi.org/10.11650/twjm/1500406383.

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Ali Hussain, Eman, and Yahya Mourad Abdul – Abbass. "On Fuzzy differential equation." Journal of Al-Qadisiyah for computer science and mathematics 11, no. 2 (August 21, 2019): 1–9. http://dx.doi.org/10.29304/jqcm.2019.11.2.540.

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In this paper, we introduce a hybrid method to use fuzzy differential equation, and Genetic Turing Machine developed for solving nth order fuzzy differential equation under Seikkala differentiability concept [14]. The Errors between the exact solutions and the approximate solutions were computed by fitness function and the Genetic Turing Machine results are obtained. After comparing the approximate solution obtained by the GTM method with approximate to the exact solution, the approximate results by Genetic Turing Machine demonstrate the efficiency of hybrid methods for solving fuzzy differential equations (FDE).
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Chang, Ick-Soon, and Sheon-Young Kang. "Fredholm integral equation method for the integro-differential Schrödinger equation." Computers & Mathematics with Applications 56, no. 10 (November 2008): 2676–85. http://dx.doi.org/10.1016/j.camwa.2008.05.027.

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Jain, Pankaj, Chandrani Basu, and Vivek Panwar. "Reduced $pq$-Differential Transform Method and Applications." Journal of Inequalities and Special Functions 13, no. 1 (March 30, 2022): 24–40. http://dx.doi.org/10.54379/jiasf-2022-1-3.

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In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.
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Abe, Kenji, Akira Ishida, Tsuguhiro Watanabe, Yasumasa Kanada, and Kyoji Nishikawa. "HIDM-New Numerical Method for Differential Equation." Kakuyūgō kenkyū 57, no. 2 (1987): 85–95. http://dx.doi.org/10.1585/jspf1958.57.85.

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Chen, Xi, and Ying Dai. "Differential transform method for solving Richards’ equation." Applied Mathematics and Mechanics 37, no. 2 (February 2016): 169–80. http://dx.doi.org/10.1007/s10483-016-2023-8.

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Youness, Ebrahim A., Abd El-Monem A. Megahed, Elsayed E. Eladdad, and Hanem F. A. Madkour. "Min-max differential game with partial differential equation." AIMS Mathematics 7, no. 8 (2022): 13777–89. http://dx.doi.org/10.3934/math.2022759.

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<abstract><p>In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of this problem. We obtained the equivalent integral equation to the CIVP. Also, we suggested a method for solving this problem. The existence, uniqueness of the solution and the uniform convergence are discussed for the two methods.</p></abstract>
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Khalili Golmankhaneh, Alireza, and Carlo Cattani. "Fractal Logistic Equation." Fractal and Fractional 3, no. 3 (July 11, 2019): 41. http://dx.doi.org/10.3390/fractalfract3030041.

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In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving fractal differential equations and finding approximate analytical solutions. Fractal differential equations are solved by using the fractal Euler method. Furthermore, fractal logistic equations and functions are given, which are useful in modeling growth of elements in sciences including biology and economics.
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Tuluce Demiray, Seyma, Yusuf Pandir, and Hasan Bulut. "Generalized Kudryashov Method for Time-Fractional Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/901540.

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In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.
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Dissertations / Theses on the topic "Differential Equation Method de Wormald"

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Aliou, Diallo Aoudi Mohamed Habib. "Local matching algorithms on the configuration model." Electronic Thesis or Diss., Compiègne, 2023. http://www.theses.fr/2023COMP2742.

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Nous proposons une alternative à l’approche prévalente dans les algorithmes de mariage en ligne. Basés sur le choix d’un critère de mariage, nous construisons des algorithmes dits locaux. Ces algorithmes sont locaux dans le sens où chacun des individus est tour à tour soumis au critère de mariage choisi. Ce qui nous amène à démontrer que le nombre de sommets qui finissent mariés lorsque chaque individu adopte une stratégie prédéfinie est solution d’une équation différentielle ordinaire. Grâce à cette approche nous prédisons les performances et comparons deux algorithmes/stratégies. Pour émuler l'asymptotique des graphes, nous utilisons le modèle de configuration basé sur un échantillonnage de la distribution de degré du graphe d'intérêt. Et globalement notre méthode peut être vue comme une généralisation de la Differential Equation Method de Wormald. Il est à noter que l’approche en ligne se concentre principalement sur les graphes bipartis
The present thesis constructs an alternative framework to online matching algorithms on large graphs. Using the configuration model to mimic the degree distributions of large networks, we are able to build algorithms based on local matching policies for nodes. Thus, we are allowed to predict and approximate the performances of a class of matching policies given the degree distributions of the initial network. Towards this goal, we use a generalization of the differential equation method to measure valued processes. Through-out the text, we provide simulations and a comparison to the seminal work of Karp, Vazirani and Vazirani based on the prevailing viewpoint in online bipartite matching
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Akman, Makbule. "Differential Quadrature Method For Time-dependent Diffusion Equation." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1224559/index.pdf.

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This thesis presents the Differential Quadrature Method (DQM) for solving time-dependent or heat conduction problem. DQM discretizes the space derivatives giving a system of ordinary differential equations with respect to time and the fourth order Runge Kutta Method (RKM) is employed for solving this system. Stabilities of the ordinary differential equations system and RKM are considered and step sizes are arranged accordingly. The procedure is applied to several time dependent diffusion problems and the solutions are presented in terms of graphics comparing with the exact solutions. This method exhibits high accuracy and efficiency comparing to the other numerical methods.
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Shedlock, Andrew James. "A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103947.

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The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical stability issues, standard numerical methods can also give rise to spurious oscillations near these discontinuities. In this study, we consider an equivalent form of the Burgers equation given by Constantin and Iyer, whose solution can be written as the expected value of a stochastic differential equation. This equivalence is used to develop a numerical method for approximating solutions to Burgers equation. Our preliminary analysis of the algorithm reveals that it is a natural generalization of the method of characteristics and that it produces approximate solutions that actually improve as the viscosity parameter vanishes. We present three examples that compare our algorithm to a recently published reference method as well as the vanishing viscosity/entropy solution for decreasing values of the viscosity.
Master of Science
Burgers equation is a Partial Differential Equation (PDE) used to model how fluids evolve in time based on some initial condition and viscosity parameter. This viscosity parameter helps describe how the energy in a fluid dissipates. When studying partial differential equations, it is often hard to find a closed form solution to the problem, so we often approximate the solution with numerical methods. As our viscosity parameter approaches 0, many numerical methods develop problems and may no longer accurately compute the solution. Using random variables, we develop an approximation algorithm and test our numerical method on various types of initial conditions with small viscosity coefficients.
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Kurus, Gulay. "Solution Of Helmholtz Type Equations By Differential Quadarature Method." Master's thesis, METU, 2000. http://etd.lib.metu.edu.tr/upload/2/12605383/index.pdf.

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This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
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Yang, Zhengzheng. "Nonlocally related partial differential equation systems, the nonclassical method and applications." Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/44993.

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Symmetry methods are important in the analysis of differential equation (DE) systems. In this thesis, we focus on two significant topics in symmetry analysis: nonlocally related partial differential equation (PDE) systems and the application of the nonclassical method. In particular, we introduce a new systematic symmetry-based method for constructing nonlocally related PDE systems (inverse potential systems). It is shown that each point symmetry of a given PDE system systematically yields a nonlocally related PDE system. Examples include applications to nonlinear reaction-diffusion equations, nonlinear diffusion equations and nonlinear wave equations. Moreover, it turns out that from these example PDEs, one can obtain nonlocal symmetries (including some previously unknown nonlocal symmetries) from some corresponding constructed inverse potential systems. In addition, we present new results on the correspondence between two potential systems arising from two nontrivial and linearly independent conservation laws (CLs) and the relationships between local symmetries of a PDE system and those of its potential systems. We apply the nonclassical method to obtain new exact solutions of the nonlinear Kompaneets (NLK) equation u_{t}=x^{-²}(x^{⁴}(\alpha u_{x}+\beta u+\gamma u^{ ²}))_{x}, where \alpha>0, \beta\geq0 and \gamma>0 are arbitrary constants. New time-dependent exact solutions for the NLK equation u_{t}=x^{-²}(x^{⁴}(\alpha u_{x}+\gamma u^{²}))_{x}, for arbitrary constants \alpha>0, \gamma>0 are obtained. Each of these solutions is expressed in terms of elementary functions. We also consider the behaviours of these new solutions for initial conditions of physical interest. More specifically, three of these families of solutions exhibit quiescent behaviour and the other two families of solutions exhibit blow-up behaviour in finite time. Consequently, it turns out that the corresponding nontrivial stationary solutions are unstable.
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Temimi, Helmi. "A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26454.

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We propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first (m-1)-derivatives are strongly superconvergent at the end of each step. We also establish that the q-degree discontinuous solution is superconvergent at the roots of (q+1-m)-degree Jacobi polynomial on each step. Furthermore, we use these results to construct asymptotically correct a posteriori error estimates. Moreover, we design a new discontinuous Galerkin method to solve the wave equation by using a method of lines approach to separate the space and time where we first apply the classical finite element method using p-degree polynomials in space to obtain a system of second-order ordinary differential equations which is solved by our new discontinuous Galerkin method. We provide an error analysis for this new method to show that, on each space-time cell, the discontinuous Galerkin finite element solution is superconvergent at the tensor product of the shifted roots of the Lobatto polynomials in space and the Jacobi polynomial in time. Then, we show that the global L2 error in space and time is convergent. Furthermore, we are able to construct asymptotically correct a posteriori error estimates for both spatial and temporal components of errors. We validate our theory by presenting several computational results for one, two and three dimensions.
Ph. D.
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Krueger, Justin Michael. "Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/78674.

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The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the microbiota's role in a host's transition from health to disease or vice versa could lead to novel medical treatments. One of the first steps toward this understanding is modeling interaction dynamics of the microbiota, which can be exceedingly challenging given the complexity of the dynamics and difficulties in collecting sufficient data. Methods such as principal differential analysis, dynamic flux estimation, and others have been developed to overcome these challenges for ordinary differential equation models. Despite their advantages, these methods are still vastly underutilized in mathematical biology, and one potential reason for this is their sophisticated implementation. While this work focuses on applying principal differential analysis to microbiota data, we also provide comprehensive details regarding the derivation and numerics of this method. For further validation of the method, we demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data. In working with these data, we capture experimentally confirmed dynamics while also revealing potential new insights into those dynamics. We also explore how we find the forward solution of the model differential equation in the context of principal differential analysis, which amounts to a least-squares finite element method. We provide alternative ideas for how to use the least-squares finite element method to find the forward solution and share the insights we gain from highlighting this piece of the larger parameter estimation problem.
Ph. D.
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Mbroh, Nana Adjoah. "On the method of lines for singularly perturbed partial differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5679.

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Magister Scientiae - MSc
Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to recourse to numerical approaches to determine suitable approximations to the solution of such equations. For solutions possessing sharp spatial transitions (such as boundary or interior layers), standard numerical methods have shown limitations as they fail to capture large gradients. The method of lines (MOL) is one of the numerical methods used to solve PDEs. It proceeds by the discretization of all but one dimension leading to systems of ordinary di erential equations. In the case of time-dependent PDEs, the MOL consists of discretizing the spatial derivatives only leaving the time variable continuous. The process results in a system to which a numerical method for initial value problems can be applied. In this project we consider various types of singularly perturbed time-dependent PDEs. For each type, using the MOL, the spatial dimensions will be discretized in many different ways following fitted numerical approaches. Each discretisation will be analysed for stability and convergence. Extensive experiments will be conducted to confirm the analyses.
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Janssen, Micha. "A Constraint Satisfaction Approach for Enclosing Solutions to Initial Value Problems for Parametric Ordinary Differential Equations." Université catholique de Louvain, 2001. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-11042002-155822/.

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This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. Theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs. The results also indicate that the new algorithm should be significantly faster when the ODE contains many operations.
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Rockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.

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In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the global relation for the Laplace equation on domains with smooth boundary. Using properties of the F_p-transform, we show that the global relation defines a continuously invertible map between the Dirichlet and Neumann data for a given BVP for the Laplace equation. Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.
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Books on the topic "Differential Equation Method de Wormald"

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Schiesser, W. E. A compendium of partial differential equation models: Method of lines analysis with MATLAB. Cambridge: Cambridge University Press, 2009.

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C, Sorensen D., and Institute for Computer Applications in Science and Engineering., eds. An asymptotic induced numerical method for the convection-diffusion-reaction equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1988.

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N, Bellomo, and Gatignol Renée, eds. Lecture notes on the discretization of the Boltzmann equation. River Edge, NJ: World Scientific, 2003.

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United States. National Aeronautics and Space Administration., ed. Compact finite volume methods for the diffusion equation. Greensboro, NC: Dept. of Mechanical Engineering, N.C. A&T State University, 1989.

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T, Patera Anthony, Peraire Jaume, and Langley Research Center, eds. A posteriori finite element bounds for sensitivity derivatives of partial-differential-equation outputs. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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Parallel-vector equation solvers for finite element engineering applications. New York: Kluwer Academic / Plenum Publishers, 2002.

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Wang, Baoxiang. Harmonic analysis method for nonlinear evolution equations, I. Singapore: World Scientific Pub. Co., 2011.

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Sin-Chung, Chang, and United States. National Aeronautics and Space Administration., eds. The Space-time solution element method-a new numerical approach for the Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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Sin-Chung, Chang, and United States. National Aeronautics and Space Administration., eds. The Space-time solution element method-a new numerical approach for the Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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Book chapters on the topic "Differential Equation Method de Wormald"

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Sewell, Granville. "Partial Differential Equation Applications." In Analysis of a Finite Element Method, 1–21. New York, NY: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4684-6331-6_1.

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Hirsch, Francis, Christophe Profeta, Bernard Roynette, and Marc Yor. "The Stochastic Differential Equation Method." In Peacocks and Associated Martingales, with Explicit Constructions, 223–64. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1908-9_6.

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Csató, Gyula, Bernard Dacorogna, and Olivier Kneuss. "General Considerations on the Flow Method." In The Pullback Equation for Differential Forms, 255–65. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8313-9_12.

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Liao, Shijun. "Two and Three Dimensional Gelfand Equation." In Homotopy Analysis Method in Nonlinear Differential Equations, 461–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_14.

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Pellegrino, Sabrina Francesca. "A Convolution-Based Method for an Integro-Differential Equation in Mechanics." In Fractional Differential Equations, 107–20. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-7716-9_7.

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Zou, Li, Zhi Zong, Zhen Wang, and Shoufu Tian. "Differential Transform Method for the Degasperis-Procesi Equation." In Lecture Notes in Electrical Engineering, 197–203. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28744-2_25.

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Liu, Xiao-Ming, Ling Hong, and Jun Jiang. "The Transform Method to Solve Fuzzy Differential Equation via Differential Inclusions." In Advances in Fuzzy Integral and Differential Equations, 49–79. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73711-5_2.

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Dobrogowska, Alina, and Mahouton Norbert Hounkonnou. "Factorization Method and General Second Order Linear Difference Equation." In Differential and Difference Equations with Applications, 67–77. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_6.

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Lian, Yanping, Gregory J. Wagner, and Wing Kam Liu. "A Meshfree Method for the Fractional Advection-Diffusion Equation." In Meshfree Methods for Partial Differential Equations VIII, 53–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51954-8_4.

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Knabner, Peter, and Lutz Angermann. "The Finite Element Method for the Poisson Equation." In Numerical Methods for Elliptic and Parabolic Partial Differential Equations, 51–109. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79385-2_2.

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Conference papers on the topic "Differential Equation Method de Wormald"

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Mesˇtrovic´, Mladen. "Generalized Differential Quadrature Method for Burgers Equation." In ASME 2003 Pressure Vessels and Piping Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/pvp2003-1905.

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The generalized differential quadrature method as an accurate and efficient numerical method is developed for the Burgers equation. The numerical algorithm for this class of problem is presented. Differential quadrature approximation of needed derivatives is given by a weighted linear sum of the function values at grid points. Recurrence relationship is used for calculation of weighting coefficients. The calculated numerical results are compared with exact solutions to show the quality of the generalized differential quadrature solutions for each example. Numerical examples have shown accuracy of the GDQ method with relatively small computational effort.
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Mikaeilvand, Nasser, Sakineh Khakrangin, and Tofigh Allahviranloo. "Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method." In 7th conference of the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.56.

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Zhang, Xiao-yong, and Yan Li. "Generalized Laguerre Spectral Method for Ordinary Differential Equation." In 2011 Fourth International Joint Conference on Computational Sciences and Optimization (CSO). IEEE, 2011. http://dx.doi.org/10.1109/cso.2011.139.

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Xinran, Zhong, Ying Dai, and Xi Chen. "Application of Differential Transform Method in Richards' Equation." In 2016 International Forum on Energy, Environment and Sustainable Development. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/ifeesd-16.2016.27.

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Servi, Sema, Yildiray Keskin, and Galip Oturanç. "Reduced differential transform method for improved Boussinesq equation." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912601.

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Zhang, Yaping. "Neural Network Method for Solving Partial Differential Equation." In 2023 2nd International Conference on Artificial Intelligence and Autonomous Robot Systems (AIARS). IEEE, 2023. http://dx.doi.org/10.1109/aiars59518.2023.00077.

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PRITCHARD, JOCELYN, and HOWARD ADELMAN. "Differential Equation Based Method for Accurate Approximations in Optimization." In 31st Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1176.

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Chen, Luoping. "Analysis of numerical method for semilinear stochastic differential equation." In Conference on Data Science and Knowledge Engineering for Sensing Decision Support (FLINS 2018). WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813273238_0008.

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Narayanamoorthy, S., T. Manirathinam, Seunggyu Lee, and K. Thangapandi. "Fractal differential transform method for solving fuzzy logistic equation." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017200.

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Zhang, X. G., Q. Zhang, J. P. Sun, T. Wang, Z. P. Song, and J. J. Wang. "Precise transfer matrix method for solving differential equation systems." In TIM 18 PHYSICS CONFERENCE. Author(s), 2018. http://dx.doi.org/10.1063/1.5075644.

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Reports on the topic "Differential Equation Method de Wormald"

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

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Abstract:
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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