Numerical Methods For Initial Value Problems In Physics
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Numerical Methods For Ordinary Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-11
Numerical Methods For Ordinary Differential Equations written by David F. Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-11 with Mathematics categories.
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Numerical Methods For Initial Value Problems In Physics
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Author : Francisco S. Guzmán
language : en
Publisher: Springer Nature
Release Date : 2023-08-23
Numerical Methods For Initial Value Problems In Physics written by Francisco S. Guzmán and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Science categories.
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts. The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds. At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems.
Difference Methods For Initial Value Problems
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Author : Robert D. Richtmyer
language : en
Publisher:
Release Date : 2013-09
Difference Methods For Initial Value Problems written by Robert D. Richtmyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
Difference Methods For Initial Value Problems
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Author : Robert D. Richtmyer
language : en
Publisher:
Release Date : 1967-01-15
Difference Methods For Initial Value Problems written by Robert D. Richtmyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-01-15 with Mathematics categories.
Difference Methods For Initial Boundary Value Problems And Flow Around Bodies
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Author : You-lan Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Difference Methods For Initial Boundary Value Problems And Flow Around Bodies written by You-lan Zhu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.
Discrete Numerical Methods In Physics And Engineering
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Author : Greenspan
language : en
Publisher: Academic Press
Release Date : 1974-05-31
Discrete Numerical Methods In Physics And Engineering written by Greenspan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-05-31 with Computers categories.
Discrete Numerical Methods in Physics and Engineering
Chemical Modelling
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Author : Michael Springborg
language : en
Publisher: Royal Society of Chemistry
Release Date : 2010-10-05
Chemical Modelling written by Michael Springborg and has been published by Royal Society of Chemistry this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-05 with Reference categories.
Chemical Modelling: Applications and Theory comprises critical literature reviews of all aspects of molecular modelling. Molecular modelling in this context refers to modelliing the structure, properties and reactions of atoms, molecules and materials. Each chapter provides a selective review of recent literature, incorporating sufficient historical perspective for the non-specialist to gain an understanding. With chemical modelling covering such a wide range of subjects, this Specialist Periodical Report serves as the first port of call to any chemist, biochemist, materials scientist or molecular physicist needing to acquaint themselves with major developments in the area.
Nbs Special Publication
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Author :
language : en
Publisher:
Release Date : 1965
Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Weights and measures categories.
Numerical Methods For Initial Value Problems In Ordinary Differential Equations
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Author : Simeon Ola Fatunla
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Numerical Methods For Initial Value Problems In Ordinary Differential Equations written by Simeon Ola Fatunla and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.
Grid Generation Methods
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Author : Vladimir D. Liseikin
language : en
Publisher: Springer
Release Date : 2017-06-12
Grid Generation Methods written by Vladimir D. Liseikin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Science categories.
This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.