{"product_id":"numerical-methods-for-ordinary-differential-equations-isbn-9780471967583","title":"Numerical Methods for Ordinary Differential Equations","description":"\u003cp\u003eThis new book updates the exceptionally popular \u003ci\u003eNumerical Analysis of Ordinary Differential Equations\u003c\/i\u003e.\u003c\/p\u003e \u003cp\u003e\"This book is...an indispensible reference for any researcher.\"\u003cbr\u003e—\u003cb\u003eAmerican Mathematical Society on the First Edition\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFeatures:\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eNew exercises included in each chapter.\u003c\/li\u003e \u003cli\u003eAuthor is widely regarded as the world expert on Runge-Kutta methods.\u003c\/li\u003e \u003cli\u003eDidactic aspects of the book have been enhanced by interspersing the text with exercises.\u003c\/li\u003e \u003cli\u003eUpdated Bibliography.\u003c\/li\u003e \u003c\/ul\u003e Preface.\u003cbr\u003e \u003cbr\u003e 1. Differential and Difference Equations.\u003cbr\u003e \u003cbr\u003e 10. Differential Equation Problems.\u003cbr\u003e \u003cbr\u003e 11. Differential Equation Theory.\u003cbr\u003e \u003cbr\u003e 12. Difference Equation Problems.\u003cbr\u003e \u003cbr\u003e 13. Difference Equation Theory.\u003cbr\u003e \u003cbr\u003e 2. Numerical Differential Equation Methods.\u003cbr\u003e \u003cbr\u003e 20. The Euler Method.\u003cbr\u003e \u003cbr\u003e 21. Analysis of the Euler Method.\u003cbr\u003e \u003cbr\u003e 22. Generalizations of the Euler Method.\u003cbr\u003e \u003cbr\u003e 23. Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 24. Linear Multistep Methods.\u003cbr\u003e \u003cbr\u003e 25. Taylor Series Methods.\u003cbr\u003e \u003cbr\u003e 26. Hybrid Methods.\u003cbr\u003e \u003cbr\u003e 3. Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 30. Preliminaries.\u003cbr\u003e \u003cbr\u003e 31. Order Conditions.\u003cbr\u003e \u003cbr\u003e 32. Low Order Explicit Methods.\u003cbr\u003e \u003cbr\u003e 33. Runge-Kutta Methods with Error Estimates.\u003cbr\u003e \u003cbr\u003e 34. Implicit Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 35. Stability of Implicit Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 36. Implementable Implicit Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 37. Order Barriers.\u003cbr\u003e \u003cbr\u003e 38. Algebraic Properties of Runge-Kutta Methods.\u003cbr\u003e \u003cbr\u003e 39. Implementation Issues.\u003cbr\u003e \u003cbr\u003e 4. Linear Multistep Methods.\u003cbr\u003e \u003cbr\u003e 40. Preliminaries.\u003cbr\u003e \u003cbr\u003e 41. The Order of Linear Multistep Methods.\u003cbr\u003e \u003cbr\u003e 42. Errors and Error Growth.\u003cbr\u003e \u003cbr\u003e 43. Stability Characteristics.\u003cbr\u003e \u003cbr\u003e 44. Order and Stability Barriers.\u003cbr\u003e \u003cbr\u003e 45. One-leg Methods and G-stability.\u003cbr\u003e \u003cbr\u003e 46. Implementation Issues.\u003cbr\u003e \u003cbr\u003e 5. General Linear Methods.\u003cbr\u003e \u003cbr\u003e 50. Representing Methods in General Linear Form.\u003cbr\u003e \u003cbr\u003e 51. Consistency, Stability and Convergence.\u003cbr\u003e \u003cbr\u003e 52. The Stability of General Linear Methods.\u003cbr\u003e \u003cbr\u003e 53. The Order of General Linear Methods.\u003cbr\u003e \u003cbr\u003e 54. Methods with Runge-Kutta Stabiulity.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.  “I enjoyed reading this book.  It is well written and quite approachable.” (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2004c)  \u003cp\u003e\"…covers now all the material that is modern standard in this field… belongs into any mathematical library...\" (Zentralblatt Math, Vol.1040, No.09, 2004)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003eJohn Charles Butcher\u003c\/b\u003e 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.\u003c\/p\u003e \u003cp\u003eIn recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This book is a fully revised update of the author's classic 1987 text, Numerical Analysis of Ordinary Differential Equations, and includes more material on linear multistep methods, whilst maintaining its emphasis on Runge-Kutta methods. It contains introductory material on differential and difference equations, and a comprehensive review of numerical methods and their potential applications. The review starts from the Euler method applied to simple problems and builds on these ideas to introduce increasingly complex methods and problems. The author then explores Runge-Kutta, linear multistep and general linear methods in detail.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eProvides a comprehensive introduction to numerical methods for solving ordinary differential equations.\u003c\/li\u003e \u003cli\u003eFeatures introductory material on differential and difference equations.\u003c\/li\u003e \u003cli\u003eIncludes detailed coverage of Runge-Kutta, linear multistep, and general linear methods.\u003c\/li\u003e \u003cli\u003eContains exercises integrated into each chapter, enabling use as a course text or for self-study.\u003cbr\u003e* Balances informal discussion with a rigorous mathematical style.\u003c\/li\u003e \u003cli\u003eWritten by a leading authority on numerical methods.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eResearchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving ordinary differential equations. It stands out amongst other books on the subject because of the author's lucid writing style, and the integrated presentation of theory, examples, and exercises.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989702426853,"sku":"NP9780471967583","price":191.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471967583.jpg?v=1761785167","url":"https:\/\/k12savings.com\/products\/numerical-methods-for-ordinary-differential-equations-isbn-9780471967583","provider":"K12savings","version":"1.0","type":"link"}