Numerical Solution of Ordinary and Partial Differential Equations
Based on a Summer School Held in Oxford, August-September 1961
Published on 15. May 2014
520 pages
978-1-4831-4947-9 (ISBN)
Description
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.
More details
Content
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 EquationsII. 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 EquationIII. 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 EquationsIV. 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 References Index
