J. C. Butcher

Numerical Methods for Ordinary Differential Equations

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 440
• Erscheinungstermin: 18. Juli 2003
• Englisch
• Abmessung: 240mm x 161mm x 28mm
• Gewicht: 830g
• ISBN-13: 9780471967583
• ISBN-10: 0471967580
• Artikelnr.: 11763740

Autorenporträt

John Charles Butcher ONZM is a New Zealand mathematician who specialises in numerical methods for the solution of ordinary differential equations. Butcher works on multistage methods for initial value problems, such as Runge-Kutta and general linear methods.

Inhaltsangabe

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.

Rezensionen

"I enjoyed reading this book. It is well written and quite approachable." ( Mathematical Reviews , 2004c)
"...covers now all the material that is modern standard in this field... belongs into any mathematical library..." (Zentralblatt Math, Vol.1040, No.09, 2004)