Mathematical And Numerical Studies Of Nonstandard Difference Equation Models Of Differential Equations Final Technical Report September 1995 September 1997
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Mathematical And Numerical Studies Of Nonstandard Difference Equation Models Of Differential Equations Final Technical Report September 1995 September 1997
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Author :
language : en
Publisher:
Release Date : 1997
Mathematical And Numerical Studies Of Nonstandard Difference Equation Models Of Differential Equations Final Technical Report September 1995 September 1997 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
The major thrust of this proposal was to continue our investigations of so-called non-standard finite-difference schemes as formulated by other authors. These schemes do not follow the standard rules used to model continuous differential equations by discrete difference equations. The two major aspects of this procedure consist of generalizing the definition of the discrete derivative and using a nonlocal model (on the computational grid or lattice) for nonlinear terms that may occur in the differential equations. Our aim was to investigate the construction of nonstandard finite-difference schemes for several classes of ordinary and partial differential equations. These equations are simple enough to be tractable, yet, have enough complexity to be both mathematically and scientifically interesting. It should be noted that all of these equations differential equations model some physical phenomena under an appropriate set of experimental conditions. The major goal of the project was to better understand the process of constructing finite-difference models for differential equations. In particular, it demonstrates the value of using nonstandard finite-difference procedures. A secondary goal was to construct and study a variety of analytical techniques that can be used to investigate the mathematical properties of the obtained difference equations. These mathematical procedures are of interest in their own right and should be a valuable contribution to the mathematics research literature in difference equations. All of the results obtained from the research done under this project have been published in the relevant research/technical journals or submitted for publication. Our expectation is that these results will lead to improved finite difference schemes for the numerical integration of both ordinary and partial differential equations. Section G of the Appendix gives a concise summary of the major results obtained under funding by the grant.
Vesa
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Author :
language : en
Publisher:
Release Date : 1926
Vesa written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1926 with categories.
International Aerospace Abstracts
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Author :
language : en
Publisher:
Release Date : 1997
International Aerospace Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Aeronautics categories.
Subject Guide To Books In Print
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Author :
language : en
Publisher:
Release Date : 1971
Subject Guide To Books In Print written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with American literature categories.
Nonstandard Finite Difference Schemes Methodology And Applications
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 2020-11-11
Nonstandard Finite Difference Schemes Methodology And Applications written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-11 with Mathematics categories.
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Advances In The Applications Of Nonstandard Finite Diffference Schemes
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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2005
Advances In The Applications Of Nonstandard Finite Diffference Schemes written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.
Differential Equations And Numerical Mathematics
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Author : G. I. Marchuk
language : en
Publisher: Elsevier
Release Date : 2014-06-25
Differential Equations And Numerical Mathematics written by G. I. Marchuk and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-25 with Mathematics categories.
Differential Equations and Numerical Mathematics contains selected papers presented in a national conference held in Novosibirsk on September 1978. This book, as the conference, is organized into three sections. Section A describes the modern theory of efficient cubature formulas; embedding theorems; and problems of spectral analysis. Section B considers the theoretical questions of partial differential equations, with emphasis on hyperbolic equations and systems, formulations, and methods for nonclassical problems of mathematical physics. Section C addresses the various problems of numerical mathematics, with focus on the optimum and asymptotically optimum algorithms for solving the problems of numerical mathematics.
Differential Equations And Mathematical Physics
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Author : Rudi Weikard
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Differential Equations And Mathematical Physics written by Rudi Weikard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume contains the proceedings of the 1999 International Conference on Differential Equations and Mathematical Physics. The contributions selected for this volume represent some of the most important presentations by scholars from around the world on developments in this area of research. The papers cover topics in the general area of linear and nonlinear differential equations and their relation to mathematical physics, such as multiparticle Schrödinger operators, stability of matter, relativity theory, fluid dynamics, spectral and scattering theory including inverse problems. Titles in this series are co-published with International Press, Cambridge, MA.
Numerical Methods For Ordinary Differential Equations
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Author : Alfredo Bellen
language : en
Publisher: Springer
Release Date : 2006-11-14
Numerical Methods For Ordinary Differential Equations written by Alfredo Bellen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Advances In Differential Equations And Mathematical Physics
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Author : Eric Carlen
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Advances In Differential Equations And Mathematical Physics written by Eric Carlen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The text offers a combination of certain emerging topics and important research advances in the area of differential equations. The topics range widely and include magnetic Schroedinger operators, the Boltzmann equations, nonlinear variational problems and noncommutative probability theory. The text is suitable for graduate and advanced graduate courses and seminars on the topic, as well as research mathematicians and physicists working in mathematical physics, applied mathematics, analysis and differential equations.