Solving ODEs with MATLAB

L. F. Shampine, I. Gladwell, S. Thompson9780521824040, 0521824044

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.

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Table of contents :
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