Numerical Solution of Ordinary Differential Equations

1. Front Matter

   Pages i-xi

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2. Introduction

   • L. Fox, D. F. Mayers

   Pages 1-13

3. Sensitivity analysis: inherent instability

   • L. Fox, D. F. Mayers

   Pages 14-41

4. Initial-value problems: one-step methods

   • L. Fox, D. F. Mayers

   Pages 42-77

5. Initial-value problems: multi-step methods

   • L. Fox, D. F. Mayers

   Pages 78-97

6. Initial-value methods for boundary-value problems

   • L. Fox, D. F. Mayers

   Pages 98-127

7. Global (finite-difference) methods for boundary-value problems

   • L. Fox, D. F. Mayers

   Pages 128-178

8. Expansion methods

   • L. Fox, D. F. Mayers

   Pages 179-197

9. Algorithms

   • L. Fox, D. F. Mayers

   Pages 198-211

10. Further notes and bibliography

    • L. Fox, D. F. Mayers

    Pages 212-230

11. Answers to selected exercises

    • L. Fox, D. F. Mayers

    Pages 231-246

12. Back Matter

    Pages 247-249

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Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numerical solution ofordinary differential equations, numerical solution of partial differential equations, and so on. These are needed because our numerical education and software have improved and because our relevant problems exhibit more variety and more difficulty. Ordinary differential equa­ tions are obvious candidates for such treatment, and the current book is written in this sense.

• differential equation
• ordinary differential equation
• ordinary differential equations

• Oxford University, UK

  L. Fox, D. F. Mayers

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