Numerical Methods For Differential Systems

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Introduction to Numerical Methods in Differential Equations

Mark H. Holmes
Introduction to Numerical Methods in Differential Equations Book PDF

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 52,7 Mb
Release : 2007-04-05
Category : Mathematics
ISBN : 9780387681214

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Introduction to Numerical Methods in Differential Equations by Mark H. Holmes Pdf

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

Numerical Methods for Ordinary Differential Equations

David F. Griffiths,Desmond J. Higham
Numerical Methods for Ordinary Differential Equations Book PDF

Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 44,9 Mb
Release : 2010-11-11
Category : Mathematics
ISBN : 9780857291486

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Numerical Methods for Ordinary Differential Equations by David F. Griffiths,Desmond J. Higham Pdf

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 Differential Equations

J.R. Dormand
Numerical Methods for Differential Equations Book PDF

Author : J.R. Dormand
Publisher : CRC Press
Page : 385 pages
File Size : 41,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083553

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Numerical Methods for Differential Equations by J.R. Dormand Pdf

With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 442 pages
File Size : 53,5 Mb
Release : 2004-08-20
Category : Mathematics
ISBN : 9780470868263

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Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.

Numerical Solution of Ordinary Differential Equations

Kendall Atkinson,Weimin Han,David E. Stewart
Numerical Solution of Ordinary Differential Equations Book PDF

Author : Kendall Atkinson,Weimin Han,David E. Stewart
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 50,9 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118164525

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Numerical Solution of Ordinary Differential Equations by Kendall Atkinson,Weimin Han,David E. Stewart Pdf

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Analytic Methods for Partial Differential Equations

G. Evans,J. Blackledge,P. Yardley
Analytic Methods for Partial Differential Equations Book PDF

Author : G. Evans,J. Blackledge,P. Yardley
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447103790

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Analytic Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

A First Course in the Numerical Analysis of Differential Equations

Arieh Iserles
A First Course in the Numerical Analysis of Differential Equations Book PDF

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 481 pages
File Size : 40,7 Mb
Release : 2008-11-27
Category : Mathematics
ISBN : 9781139473767

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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles Pdf

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 546 pages
File Size : 50,7 Mb
Release : 2016-08-29
Category : Mathematics
ISBN : 9781119121503

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Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

Ernst Hairer,Christian Lubich,Michel Roche
The Numerical Solution of Differential Algebraic Systems by Runge Kutta Methods Book PDF

Author : Ernst Hairer,Christian Lubich,Michel Roche
Publisher : Springer
Page : 146 pages
File Size : 51,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468325

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods by Ernst Hairer,Christian Lubich,Michel Roche Pdf

The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.

Numerical Methods for Partial Differential Equations

Vitoriano Ruas
Numerical Methods for Partial Differential Equations Book PDF

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 54,8 Mb
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 9781119111368

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Numerical Methods for Partial Differential Equations by Vitoriano Ruas Pdf

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Numerical Solution of Ordinary Differential Equations

L.F. Shampine
Numerical Solution of Ordinary Differential Equations Book PDF

Author : L.F. Shampine
Publisher : Routledge
Page : 632 pages
File Size : 52,8 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9781351427555

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Numerical Solution of Ordinary Differential Equations by L.F. Shampine Pdf

This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Numerical Solution of Stochastic Differential Equations

Peter E. Kloeden,Eckhard Platen
Numerical Solution of Stochastic Differential Equations Book PDF

Author : Peter E. Kloeden,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 49,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662126165

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Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden,Eckhard Platen Pdf

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Robust Numerical Methods for Singularly Perturbed Differential Equations

Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Robust Numerical Methods for Singularly Perturbed Differential Equations Book PDF

Author : Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 599 pages
File Size : 53,7 Mb
Release : 2008-09-17
Category : Mathematics
ISBN : 9783540344674

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Robust Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Advanced Numerical Methods for Differential Equations

Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Advanced Numerical Methods for Differential Equations Book PDF

Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Publisher : CRC Press
Page : 336 pages
File Size : 43,9 Mb
Release : 2021-07-29
Category : Mathematics
ISBN : 9781000381085

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Advanced Numerical Methods for Differential Equations by Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar Pdf

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Peter Knabner,Lutz Angerman
Numerical Methods for Elliptic and Parabolic Partial Differential Equations Book PDF

Author : Peter Knabner,Lutz Angerman
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 46,8 Mb
Release : 2006-05-26
Category : Mathematics
ISBN : 9780387217628

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Numerical Methods for Elliptic and Parabolic Partial Differential Equations by Peter Knabner,Lutz Angerman Pdf

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.