Differential Equations And Numerical Analysis

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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 : 46,8 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.

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 : 44,8 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

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

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 442 pages
File Size : 52,5 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.

Partial Differential Equations with Numerical Methods

Stig Larsson,Vidar Thomee
Partial Differential Equations with Numerical Methods Book PDF

Author : Stig Larsson,Vidar Thomee
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 44,7 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9783540887058

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Partial Differential Equations with Numerical Methods by Stig Larsson,Vidar Thomee Pdf

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

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 : 48,7 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 Analysis of Partial Differential Equations

S. H, Lui
Numerical Analysis of Partial Differential Equations Book PDF

Author : S. H, Lui
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 43,7 Mb
Release : 2012-01-10
Category : Mathematics
ISBN : 9781118111116

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Numerical Analysis of Partial Differential Equations by S. H, Lui Pdf

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

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 : 51,9 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.

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 : 43,9 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.

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 : 44,9 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

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

Author : A. Iserles
Publisher : Cambridge University Press
Page : 402 pages
File Size : 44,5 Mb
Release : 1996-01-18
Category : Mathematics
ISBN : 0521556554

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A First Course in the Numerical Analysis of Differential Equations by A. 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 point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations.

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 : 49,6 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 Nonlinear Partial Differential Equations

Sören Bartels
Numerical Methods for Nonlinear Partial Differential Equations Book PDF

Author : Sören Bartels
Publisher : Springer
Page : 394 pages
File Size : 46,5 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971

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Numerical Methods for Nonlinear Partial Differential Equations by Sören Bartels Pdf

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

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 : 426 pages
File Size : 48,6 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.

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 : 49,9 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 Analysis of Partial Differential Equations Using Maple and MATLAB

Martin J. Gander,Felix Kwok
Numerical Analysis of Partial Differential Equations Using Maple and MATLAB Book PDF

Author : Martin J. Gander,Felix Kwok
Publisher : SIAM
Page : 163 pages
File Size : 44,9 Mb
Release : 2018-01-01
Category : Science
ISBN : 9781611975307

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Numerical Analysis of Partial Differential Equations Using Maple and MATLAB by Martin J. Gander,Felix Kwok Pdf

This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.