Numerical Solution of Ordinary and Partial Differential Equations - 1st Edition - ISBN: 9780080096605, 9781483149479

Numerical Solution of Ordinary and Partial Differential Equations

1st Edition

Based on a Summer School Held in Oxford, August-September 1961

Authors: L. Fox
eBook ISBN: 9781483149479
Imprint: Pergamon
Published Date: 1st January 1962
Page Count: 520
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Numerical Solution of Ordinary and Partial Differential Equations is based on a summer school held in Oxford in August-September 1961.

The book is organized into four parts. The first three cover the numerical solution of ordinary differential equations, integral equations, and partial differential equations of quasi-linear form. Most of the techniques are evaluated from the standpoints of accuracy, convergence, and stability (in the various senses of these terms) as well as ease of coding and convenience of machine computation. The last part, on practical problems, uses and develops the techniques for the treatment of problems of the greatest difficulty and complexity, which tax not only the best machines but also the best brains.

This book was written for scientists who have problems to solve, and who want to know what methods exist, why and in what circumstances some are better than others, and how to adapt and develop techniques for new problems. The budding numerical analyst should also benefit from this book, and should find some topics for valuable research. The first three parts, in fact, could be used not only by practical men but also by students, though a preliminary elementary course would assist the reading.

Table of Contents

I. Ordinary Differential Equations

1. Ordinary Differential Equations and Finite Differences

2. Methods of Runge-Kutta Type

3. Prediction and Correction: Deferred Correction

4. Stability of Step-By-Step Methods

5. Boundary-Value Problems and Methods

6. Eigenvalue Problems

7. Application to the One-Dimensional Schrödinger Equation

8. Accuracy and Precision of Methods

9. Chebyshev Approximation

10. Chebyshev Solution of Ordinary Differential Equations

II. Integral Equations

11. Fredholm Equations of Second Kind

12. Fredholm Equations of First and Third Kinds

13. Equations of Volterra Type

14. Singular and Non-Linear Integral Equations

15. Integro-Differential Equations in Nuclear Collision Problems

16. Roothaan's Procedure for Solving the Hartree-Fock Equation

III. Introduction to Partial Differential Equations

17. General Classification. Hyperbolic Equations and Characteristics

18. Finite-Difference Methods for Hyperbolic Equations

19. Parabolic Equations in Two Dimensions: I

20. Parabolic Equations in Two Dimensions: II

21. Finite-Difference Formula for Elliptic Equations in Two Dimensions

22. Direct Solution of Elliptic Finite-Difference Equations

23. Iterative Solution of Elliptic Finite-Difference Equations

24. Singularities in Elliptic Equations

IV. Practical Problems in Partial Differential Equations

25. Elliptic Equations in Nuclear Reactor Problems

26. Solution by Characteristics of the Equations of One-Dimensional Unsteady Flow

27. Finite-Difference Methods for One-Dimensional Unsteady Flow

28. Characteristics in Three Independent Variables

29. Quasi-Linear Parabolic Equations in More Than Two Dimensions: I

30. Quasi-Linear Parabolic Equations in More Than Two Dimensions: II

31. The Linear Transport Equation in One and Two Dimensions

32. Monte Carlo Methods for Neutronics Problems

33. Special Techniques of the Monte Carlo Method

34. Some Problems in Plasma Physics

35. Self-Consistent Solutions of a Non-Linear Problem in Plasma Physics

36. Numerical Weather Prediction




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About the Author

L. Fox

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