Numerical Solution of Ordinary and Partial Differential Equations

Numerical Solution of Ordinary and Partial Differential Equations

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

1st Edition - January 1, 1962

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  • Author: L. Fox
  • eBook ISBN: 9781483149479

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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



Product details

  • No. of pages: 520
  • Language: English
  • Copyright: © Pergamon 1962
  • Published: January 1, 1962
  • Imprint: Pergamon
  • eBook ISBN: 9781483149479

About the Author

L. Fox

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