Numerical Methods for Ordinary Differential Equations 3rd edition by Butcher – Ebook PDF Instant Download/Delivery: 1119121507, 978-1119121503
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ISBN 10: 1119121507
ISBN 13: 978-1119121503
Author: Butcher
A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject
The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics.
In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems.
This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
Numerical Methods for Ordinary Differential Equations 3rd Table of contents:
Chapter 1: Differential and Difference Equations
10 Differential Equation Problems
11 Differential Equation Theory
12 Further Evolutionary Problems
13 Difference Equation Problems
14 Difference Equation Theory
15 Location of Polynomial Zeros
Chapter 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 Multivalue Mulitistage Methods
27 Introduction to Implementation
Chapter 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 Implementation Issues
38 Algebraic Properties of Runge–Kutta Methods
39 Symplectic Runge–Kutta Methods
Chapter 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
Chapter 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 stability
55 Methods with Inherent Runge–Kutta Stability
56 G-symplectic methods
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