Solving ODEs with MATLAB

This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples. Cover Page......Page 1 Solving ODEs with MATLAB......Page 3 Title Page......Page 5 ISBN 0521824044......Page 6 3 Boundary Value Problems......Page 7 4 Delay Differential Equations......Page 8 Preface......Page 9 1.1 Introduction......Page 11 1.2 Existence, Uniqueness, and Well-Posedness......Page 16 1.3 Standard Form......Page 29 1.4 Control of the Error......Page 37 1.5 Qualitative Properties......Page 44 2.1 Introduction......Page 49 2.2 Numerical Methods for IVPs......Page 50 2.2.1 One-Step Methods......Page 51 2.2.2 Methods with Memory......Page 67 2.3 Solving IVPs in MATLAB......Page 91 2.3.1 Event Location......Page 102 2.3.2 ODEs Involving a Mass Matrix......Page 115 2.3.3 Large Systems and the Method of Lines......Page 124 2.3.4 Singularities......Page 137 3.1 Introduction......Page 143 3.2 Boundary Value Problems......Page 145 3.3 Boundary Conditions......Page 148 3.3.1 Boundary Conditions at Singular Points......Page 149 3.3.2 Boundary Conditions at Infinity......Page 156 3.4 Numerical Methods for BVPs......Page 166 3.5 Solving BVPs in MATLAB......Page 178 4.1 Introduction......Page 223 4.2 Delay Differential Equations......Page 224 4.3 Numerical Methods for DDEs......Page 227 4.4 Solving DDEs in MATLAB......Page 231 4.5 Other Kinds of DDEs and Software......Page 257 Bibliography......Page 261 C......Page 267 I......Page 268 L,M......Page 269 O......Page 271 P......Page 272 Q,S,T,V,W......Page 273 Cover Page 1 Solving ODEs with MATLAB 3 Title Page 5 ISBN 0521824044 6 Contents (with page links) 7 1 Getting Started 7 2 Initial Value Problems 7 3 Boundary Value Problems 7 4 Delay Differential Equations 8 Preface 9 Chapter 1 Getting Started 11 1.1 Introduction 11 1.2 Existence, Uniqueness, and Well-Posedness 16 1.3 Standard Form 29 1.4 Control of the Error 37 1.5 Qualitative Properties 44 Chapter 2 Initial Value Problems 49 2.1 Introduction 49 2.2 Numerical Methods for IVPs 50 2.2.1 One-Step Methods 51 2.2.2 Methods with Memory 67 2.3 Solving IVPs in MATLAB 91 2.3.1 Event Location 102 2.3.2 ODEs Involving a Mass Matrix 115 2.3.3 Large Systems and the Method of Lines 124 2.3.4 Singularities 137 Chapter 3 Boundary Value Problems 143 3.1 Introduction 143 3.2 Boundary Value Problems 145 3.3 Boundary Conditions 148 3.3.1 Boundary Conditions at Singular Points 149 3.3.2 Boundary Conditions at Infinity 156 3.4 Numerical Methods for BVPs 166 3.5 Solving BVPs in MATLAB 178 Chapter 4 Delay Differential Equations 223 4.1 Introduction 223 4.2 Delay Differential Equations 224 4.3 Numerical Methods for DDEs 227 4.4 Solving DDEs in MATLAB 231 4.5 Other Kinds of DDEs and Software 257 Bibliography 261 Index 267 A,B 267 C 267 D 268 E,F 268 G 268 I 268 L,M 269 O 271 P 272 Q,S,T,V,W 273 This Book Is For People Who Need To Solve Ordinary Differential Equations (odes), Both Initial Value Problems (ivps) And Boundary Value Problems (bvps) As Well As Delay Differential Equations (ddes). These Topics Are Usually Taught In Separate Courses Of Length One Semester Each, But Solving Odes With Matlab Provides A Sound Treatment Of All Three In About 250 Pages. The Chapters On Each Of These Topics Begin With A Discussion Of The Facts Of Life For The Problem, Mainly By Means Of Examples. Numerical Methods For The Problem Are Then Developed - But Only The Methods Most Widely Used. Although The Treatment Of Each Method Is Brief And Technical Issues Are Minimized, The Issues Important In Practice And For Understanding The Codes Are Discussed. Often Solving A Real Problem Is Much More Than Just Learning How To Call A Code. The Last Part Of Each Chapter Is A Tutorial That Shows How To Solve Problems By Means Of Small But Realistic Examples.--jacket. Getting Started -- Initial Value Problems -- Boundary Value Problems -- Delay Differential Equations. L.f. Shampine, I. Gladwell, S. Thompson. Includes Bibliographical References (p. 251-256) And Index. This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples. Ordinary differential equations (ODEs) are used throughout engineering, mathematics, and science to describe how physical quantities change, so an introductory course on elementary ODEs and their solutions is a standard part of the curriculum in these fields.