Numerical Methods for Ordinary Differential Equations

This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher." —American Mathematical Society on the First Edition Features: New exercises included in each chapter. Author is widely regarded as the world expert on Runge-Kutta methods. Didactic aspects of the book have been enhanced by interspersing the text with exercises. Updated Bibliography.

Preface. 1. Differential and Difference Equations. 10. Differential Equation Problems. 11. Differential Equation Theory. 12. Difference Equation Problems. 13. Difference Equation Theory. 2. Numerical Differential Equation Methods. 20. The Euler Method. 21. Analysis of the Euler Method. 22. Generalizations of the Euler Method. 23. Runge-Kutta Methods. 24. Linear Multistep Methods. 25. Taylor Series Methods. 26. Hybrid Methods. 3. Runge-Kutta Methods. 30. Preliminaries. 31. Order Conditions. 32. Low Order Explicit Methods. 33. Runge-Kutta Methods with Error Estimates. 34. Implicit Runge-Kutta Methods. 35. Stability of Implicit Runge-Kutta Methods. 36. Implementable Implicit Runge-Kutta Methods. 37. Order Barriers. 38. Algebraic Properties of Runge-Kutta Methods. 39. Implementation Issues. 4. Linear Multistep Methods. 40. Preliminaries. 41. The Order of Linear Multistep Methods. 42. Errors and Error Growth. 43. Stability Characteristics. 44. Order and Stability Barriers. 45. One-leg Methods and G-stability. 46. Implementation Issues. 5. General Linear Methods. 50. Representing Methods in General Linear Form. 51. Consistency, Stability and Convergence. 52. The Stability of General Linear Methods. 53. The Order of General Linear Methods. 54. Methods with Runge-Kutta Stabiulity. References. Index.