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Academic literature on the topic 'Numerical solutions'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Numerical solutions"

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ROTARU, Constantin. "NUMERICAL SOLUTIONS FOR COMBUSTION WAVE VELOCITY." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 21, no. 1 (October 8, 2019): 184–93. http://dx.doi.org/10.19062/2247-3173.2019.21.25.

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Attwood, G. B., and David Tall. "Numerical Solutions of Equations." Mathematical Gazette 78, no. 481 (March 1994): 77. http://dx.doi.org/10.2307/3619449.

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Xinfu, Chen, Charlie M. Elliot, Gardiner Andy, and Jennifer Jing Zhao. "Convergence of numerical solutions." Applicable Analysis 69, no. 1-2 (June 1998): 95–108. http://dx.doi.org/10.1080/00036819808840645.

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Demidov, A. S. "Inverse, ill-posed problems, essentially different solutions and explicit formulas for solutions." Journal of Physics: Conference Series 2092, no. 1 (December 1, 2021): 012016. http://dx.doi.org/10.1088/1742-6596/2092/1/012016.

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Abstract A request for an inverse problem, as well as for an incorrect problem produces tens of millions of answers in the Internet. In the past few decades, hundreds of international conferences on these topics have been held annually. Problems of this kind are quite involved, and their numerical analysis requires the development of special methods and numerical algorithms. Explicit formulas provide the main tool for testing these methods and numerical algorithms. The Cauchy problem for an elliptic equation is a classical ill-posed problem, which serves as a model for many inverse and incorrect problems. In the present paper we give a numerically realizable explicit formula for solving the Cauchy problem in a two-dimensional domain for a general second-order linear elliptic equation with analytic coefficients and the Cauchy analytic data on the analytic boundary.
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Wu, G., Eric Wai Ming Lee, and Gao Li. "Numerical solutions of the reaction-diffusion equation." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 2 (March 2, 2015): 265–71. http://dx.doi.org/10.1108/hff-04-2014-0113.

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Purpose – The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels. Design/methodology/approach – Using the discrete numerical integral formula, the general way is given to solve the famous reaction-diffusion equation numerically. Findings – With the given explicit solution, the results show the conveniences of the general numerical schemes and numerical simulation of the reaction-diffusion is finally presented in the cases of various coefficients. Originality/value – The method avoids the treatment of the time derivative as that in the classical finite difference method and the VIM is introduced to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations.
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Isakari, Shirley M., and Richard C. J. Somerville. "Accurate numerical solutions for Daisyworld." Tellus B: Chemical and Physical Meteorology 41, no. 4 (July 1989): 478–82. http://dx.doi.org/10.3402/tellusb.v41i4.15103.

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ISAKARI, SHIRLEY M., and RICHARD C. J. SOMERVILLE. "Accurate numerical solutions for Daisyworld." Tellus B 41B, no. 4 (September 1989): 478–82. http://dx.doi.org/10.1111/j.1600-0889.1989.tb00324.x.

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Rioux, Frank. "Numerical solutions for Schroedinger's equation." Journal of Chemical Education 67, no. 9 (September 1990): 770. http://dx.doi.org/10.1021/ed067p770.1.

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Laponin, V. S., N. P. Savenkova, and V. P. Il’yutko. "Numerical method for soliton solutions." Computational Mathematics and Modeling 23, no. 3 (July 2012): 254–65. http://dx.doi.org/10.1007/s10598-012-9135-0.

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Galiyev, Sh I. "Numerical solutions of minmaxmin problems." USSR Computational Mathematics and Mathematical Physics 28, no. 4 (January 1988): 25–32. http://dx.doi.org/10.1016/0041-5553(88)90107-3.

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Dissertations / Theses on the topic "Numerical solutions"

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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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Briggs, A. J. "Numerical solutions of Hamilton-Jacobi equations." Thesis, University of Sussex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668.

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Van, Cong Tuan Son. "Numerical solutions to some inverse problems." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38248.

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Doctor of Philosophy
Department of Mathematics
Alexander G. Ramm
In this dissertation, the author presents two independent researches on inverse problems: (1) creating materials in which heat propagates a long a line and (2) 3D inverse scattering problem with non-over-determined data. The theories of these methods were developed by Professor Alexander Ramm and are presented in Chapters 1 and 3. The algorithms and numerical results are taken from the papers of Professor Alexander Ramm and the author and are presented in Chapters 2 and 4.
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Zeineddin, Rafik Paul. "Numerical electromagnetics codes problems, solutions and applications." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1176315682.

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Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.

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Iafrati, Alessandro. "Floating body impact : asymptotic and numerical solutions." Thesis, University of East Anglia, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501123.

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This thesis is concerned with the estimate of hydrodynamic loads generated during the water entry of bodies, originally floating on a still liquid surface. The analysis assumes the fluid to be ideal and the flow potential. The liquid is treated as incompressible, but the effects of weak compressibility are carefully estimated. A theoretical estimate of the loads in the early stage after the sudden start of the vertical downward motion of the body is derived. The solution is achieved through the method of matched asymptotic expansions, by using the non-dimensional body displacement as a small parameter. A uniformly valid solution is obtained by formulating an inner problem under suitable set of stretched variables and by matching its asymptotic behaviour with the inner limit of the outer solution. The boundary value problem governing the inner solution is strongly nonlinear, with nonlinear boundary conditions imposed on unknown free surface position. The solution is obtained through suitably developed numerical iterative procedures.
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Tang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.

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Hoang, Nguyen Si. "Numerical solutions to some ill-posed problems." Diss., Kansas State University, 2011. http://hdl.handle.net/2097/9204.

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Doctor of Philosophy
Department of Mathematics
Alexander G. Ramm
Several methods for a stable solution to the equation $F(u)=f$ have been developed. Here $F:H\to H$ is an operator in a Hilbert space $H$, and we assume that noisy data $f_\delta$, $\|f_\delta-f\|\le \delta$, are given in place of the exact data $f$. When $F$ is a linear bounded operator, two versions of the Dynamical Systems Method (DSM) with stopping rules of Discrepancy Principle type are proposed and justified mathematically. When $F$ is a non-linear monotone operator, various versions of the DSM are studied. A Discrepancy Principle for solving the equation is formulated and justified. Several versions of the DSM for solving the equation are formulated. These methods consist of a Newton-type method, a gradient-type method, and a simple iteration method. A priori and a posteriori choices of stopping rules for these methods are proposed and justified. Convergence of the solutions, obtained by these methods, to the minimal norm solution to the equation $F(u)=f$ is proved. Iterative schemes with a posteriori choices of stopping rule corresponding to the proposed DSM are formulated. Convergence of these iterative schemes to a solution to the equation $F(u)=f$ is proved. This dissertation consists of six chapters which are based on joint papers by the author and his advisor Prof. Alexander G. Ramm. These papers are published in different journals. The first two chapters deal with equations with linear and bounded operators and the last four chapters deal with non-linear equations with monotone operators.
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D'Alessandro, Valerio. "Numerical solutions of turbulent flows: industrial applications." Doctoral thesis, Università Politecnica delle Marche, 2013. http://hdl.handle.net/11566/242718.

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La Computational Fluid-Dynamics (CFD) si trova sempre maggiormente coinvolta nello studio di sistemi energetici innovativi. Quindi è logico pensare a filoni di ricerca in cui si sviluppano metodi numerici efficienti, robusti ed accurati per la soluzione di tali problemi. In questa tesi si affronta la soluzione numerica di alcuni problemi di interesse industriale sia con tecniche risolutive standard che innovative. In particolare sono stati sviluppati solutori ad elavato ordine di accuratezza per flussi incomprimibili basati sul metodo ad elementi finiti discontinui di Galerkin (DG). Il metodo DG è basato su approssimazioni polinomiali all’interno del singolo elemento computazionale senza richiesta di continuità globale della soluzione. Recentemente tale metodo sta ricevendo particolare interesse per l’applicazione a problemi di CFD. Partendo da un codice presistente 2D viscoso, basato su un flusso a comprimibilità artificiale, è stata sviluppata una versione 3D che si sta dimostrando capace di essere utilizata come solutore DNS. Quindi è stato aggiunto il modello di turbolenza di Spalart-Allmaras (SA) sia sulla versione 2D che 3D. Vale la pena notare che la soluzione DG delle equazioni RANS è molto complessa per via dell’enorme rigidezza numerica del problema. In questo lavoro viene proposta un’implementazione innovativa del modello SA che modifica opportunamente i termini sorgenti e diffusivi dell’equazione di evoluzione SA quando la variabile di lavoro, o una delle funzioni di chiusura del modello, diventano negative. E’ importante notare che ad oggi in letteratura non sono presenti lavori che trattano della soluzione DG del sistema di equazioni RANS-SA incomprimibili. L’approccio proposto è stato quindi testato su un’ampia gamma di problemi. Parallelamente è stata studiata sia l’Aerodinamica instazionaria dei rotori eolici di tipo Savonius che il campo di moto interno al tubo vortice ad effetto Ranque-Hilsch (RHVT) attraverso solutori standard a volumi finiti. Nonostante durante questo lavoro di tesi siano stati sviluppati solutori DG per un ampio range di numeri di Reynolds, ad oggi essi non sono stati ancora applicati a problemi come il Savonius o RHVT in quanto al tempo di quelle analisi non si disponeva dei codici allo stato di sviluppo attuale.
The study of innovative energy systems often involves complex fluid flows problems and the Computational Fluid Dynamics (CFD) is one of the main tools of analysis. It is very easy to understand as developing new high-accuracy solution techniques for the fluid flow governing equations is of an extreme interesting research area. This work is aimed in the field of numerical solution of turbulent flows problems in industrial configurations with standard and innovative discretization techquines. In this thesis great efforts were addressed in to develop of a high-order Discontinuous Galerkin (DG) solver for incompressible flows in order to enjoy its accuracy in a wide class of industrial problems. DG methods are based on polynomial approximations inside the computational elements with no global continuity requirement and they are receiving an increasing interest in CFD community. features. Starting from a 2D viscous version of a code, based on the artificial compressibility flux DG method [1], in this thesis a 3D version is presented and its suitability for DNS computations is demonstrated. Moreover the Spalart-Allmaras (SA) turbulence model has been implemented in both the 2D and 3D solvers.It is worth noting that DG space discretization of RANS equations is a difficult task due the numerical stiffness of the equations. In this work the SA model is modified in source and diffusion terms to deal with numerical instabilities coming-up when the working variable, or one of the model closure functions, become negative thus unphysical. It is important to remark that in the present literature are not reported others DG solvers for the incompressible RANSSA equations. The realiability, accuracy and robustness of the solution method was assessed computing several test-cases in simple and real-life configurations. Simultaneously unsteady Aerodynamics of the Savonius wind rotor and the flow field inside a Ranque-Hilsch vortex tube (RHVT) were extensively studied with standard finite volume solvers obtaining innovative results. Neverthless in this moment our DG solvers can cover a wide range of Reynolds numbers, they have not still found application to analyze problems as Savonius rotors or RHVT since at the time of those analysis our codes can not deal with that kind of flows.
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Cuminato, José Alberto. "Numerical solutions of Cauchy integral equations and applications." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:434954bb-bf08-448b-9e02-9948d1287e37.

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This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.
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Books on the topic "Numerical solutions"

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Cantaragiu, Ștefan. Microwave Numerical Solutions. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61209-1.

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Dukkipati, Rao V. Numerical methods. New Delhi: New Age International Ltd., 2010.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. Providence, R.I: American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. Providence, R.I: American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling waves solutions. Providence, R.I: American Mathematical Society, 2009.

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Pava, Jaime Angulo. Nonlinear dispersive equations: Existence and stability of solitary and periodic travelling wave solutions. Providence, R.I: American Mathematical Society, 2009.

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Inc, ebrary, ed. Numerical methods: Problems and solutions. 2nd ed. New Delhi: New Age International (P) Ltd., Publishers, 2004.

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K, Jain M. Numerical methods: Problems and solutions. New Delhi: New Age International, 1994.

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Laflin, S. Numerical methods of linear algebra. [London?]: Chartwell-Brat, 1988.

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Kröner, Dietmar. Numerical schemes for conservation laws. Chichester: Wiley, 1997.

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Book chapters on the topic "Numerical solutions"

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Musielak, Zdzislaw, and Billy Quarles. "Numerical Solutions." In SpringerBriefs in Astronomy, 55–70. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58226-9_4.

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Służalec, Andrzej. "Numerical Solutions." In Theory of Metal Forming Plasticity, 155–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-10449-1_11.

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Ungarish, Marius. "Numerical Solutions." In Hydrodynamics of Suspensions, 255–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-01651-0_8.

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Kakaç, Sadık, Yaman Yener, and Carolina P. Naveira-Cotta. "Numerical Solutions." In Heat Conduction, 425–62. Fifth edition. | Boca Raton : Taylor & Francis, CRC Press, [2018]: CRC Press, 2018. http://dx.doi.org/10.1201/b22157-12.

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Ramsay, James, and Giles Hooker. "Numerical Solutions." In Springer Series in Statistics, 69–81. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7190-9_5.

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de Lemos, Marcelo J. S. "Numerical Solutions." In Thermal Plug and Abandonment of Oil Wells, 79–91. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-59283-6_7.

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Alexandrov, Sergei. "Numerical Method." In Singular Solutions in Plasticity, 61–80. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5227-9_5.

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Cantaragiu, Ștefan. "Parameters of the Shielded Microstrip Line." In Microwave Numerical Solutions, 91–98. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61209-1_3.

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Cantaragiu, Ștefan. "The Study of the Electromagnetic Field from Shielded Microstrip Line Using Electrodynamic Method." In Microwave Numerical Solutions, 1–61. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61209-1_1.

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Cantaragiu, Ștefan. "Microwave Transistor Amplifier." In Microwave Numerical Solutions, 147–66. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61209-1_6.

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Conference papers on the topic "Numerical solutions"

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Zivanovic, Sanja, and Pieter Collins. "Numerical solutions to noisy systems." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717780.

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Watson, G. A., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Robust Solutions to Linear Data Fitting Problems." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790151.

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Alefeld, G. "Complementarity Problems: Error Bounds for Approximate Solutions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990973.

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De Giorgi, Luigi, Volfango Bertola, Emilio Cafaro, and Carlo Cima. "Numerical Solutions Control by Entropy Analysis." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22903.

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The rate of entropy generation is used to estimate the average error of approximate numerical solutions of conductive and convective heat transfer problems with respect to the corresponding exact solutions. This is possible because the entropy analysis of simple problems, which have exact analytical solutions, shows that the rate of entropy generation behaves similarly to the average error of approximate solutions. Two test cases (transient two-dimensional heat conduction with Dirichlet boundary conditions and free convection between two plates at different temperatures with internal heat source) are discussed. Results suggest to use entropy analysis as a tool for the assessment of solution methods and to estimate the error of numerical solutions of thermal-fluid-dynamics problems.
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Özkoç, Arzu, Ahmet Tekcan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Integer Solutions of a Special Diophantine Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637759.

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Dobkevich, Mariya, Felix Sadyrbaev, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Types of solutions and approximation of solutions of second order nonlinear boundary value problems." In 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/10.1063/1.3241443.

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Xu, Yufeng, and Om P. Agrawal. "Numerical Solutions of Generalized Oscillator Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12705.

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Harmonic oscillators play a fundamental role in many areas of science and engineering, such as classical mechanics, electronics, quantum physics, and others. As a result, harmonic oscillators have been studied extensively. Classical harmonic oscillators are defined using integer order derivatives. In recent years, fractional derivatives have been used to model the behaviors of damped systems more accurately. In this paper, we use three operators called K-, A- and B-operators to define the equation of motion of an oscillator. In contrast to fractional integral and derivative operators which use fractional power kernels or their variations in their definitions, the K-, A- and B-operators allow the kernel to be arbitrary. In the case when the kernel is a power kernel, these operators reduce to fractional integral and derivative operators. Thus, they are more general than the fractional integral and derivative operators. Because of the general nature of the K-, A- and B-operators, the harmonic oscillators are called the generalized harmonic oscillators. The equations of motion of a generalized harmonic oscillator are obtained using a generalized Euler-Lagrange equation presented recently. In general, the resulting equations cannot be solved in closed form. A numerical scheme is presented to solve these equations. To verify the effectiveness of the numerical scheme, a problem is considered for which a closed form solution could be found. Numerical solution for the problem is compared with the analytical solution. It is demonstrated that the numerical scheme is convergent, and the order of convergence is 2. For a special kernel, this scheme reduces to a scheme presented recently in the literature.
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Warren, G. M. "Numerical Solutions for Pressure Transient Analysis." In SPE Gas Technology Symposium. Society of Petroleum Engineers, 1993. http://dx.doi.org/10.2118/26177-ms.

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Wagner, Wolfgang. "Monte Carlo Methods and Numerical Solutions." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941579.

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Mixon, Dustin G., and Hans Parshall. "Exact Line Packings from Numerical Solutions." In 2019 13th International conference on Sampling Theory and Applications (SampTA). IEEE, 2019. http://dx.doi.org/10.1109/sampta45681.2019.9030933.

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Reports on the topic "Numerical solutions"

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Cao, Yanzhao. Numerical Solutions for Optimal Control under SPDE Constraints. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada479338.

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Chang, B. Analytical Solutions for Testing Ray-Effect Errors in Numerical Solutions of the Transport Equation. Office of Scientific and Technical Information (OSTI), May 2003. http://dx.doi.org/10.2172/15004539.

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Gregory, M. V. Numerical benchmarking of SPEEDUP{trademark} against point kinetics solutions. Office of Scientific and Technical Information (OSTI), February 1993. http://dx.doi.org/10.2172/10149598.

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Gregory, M. V. Numerical benchmarking of SPEEDUP[trademark] against point kinetics solutions. Office of Scientific and Technical Information (OSTI), February 1993. http://dx.doi.org/10.2172/6591681.

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Cao, Yanzhao. Numerical Solutions for Optimal Control Problems Under SPDE Constraints. Fort Belvoir, VA: Defense Technical Information Center, October 2006. http://dx.doi.org/10.21236/ada458787.

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Huang, Jeffrey. Numerical solutions of continuous wave beam in nonlinear media. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5626.

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Cao, Yanzhao. Numerical Solutions for Optimal Control Problems Under SPDE Constraints. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada480192.

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Shu, Chi Wang. High Order Numerical Methods for Long Time Solutions with Discontinuities. Fort Belvoir, VA: Defense Technical Information Center, May 2001. http://dx.doi.org/10.21236/ada396173.

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Hwang, Jing-Shiang. Numerical Solutions for Bayes Sequential Decision Approach to Bioequivalence Problem. Fort Belvoir, VA: Defense Technical Information Center, March 1991. http://dx.doi.org/10.21236/ada236707.

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Prinja, Anil K. Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report. Office of Scientific and Technical Information (OSTI), December 2000. http://dx.doi.org/10.2172/782033.

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