Numerical Methods for Ordinary Differential

Authored by one of the world's leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear methods, thus providing assistance to those who wish to develop their own computer code. Accompanied by a website hosting solutions to problems and slides for use in teaching Illustrated throughout by worked examples of key algorithms. Presents practical guidance on solving equations associated with general linear methods Gives an introductory overview of the field before going on to describe recent developments. All methods are illustrated with detailed examples and problems sets.

Contents
Preface to the first edition
Preface to the second edition	p. 1
Differential and Difference Equations	p. 10
Differential Equation Problems	p. 100
Introduction to differential equations	p. 101
The Kepler problem	p. 102
A problem arising from the method of lines	p. 103
The simple pendulum	p. 104
A chemical kinetics problem	p. 105
The Van der Pol equation and limit cycles	p. 106
The Lotka-Volterra problem and periodic orbits	p. 107
The Euler equations of rigid body rotation	p. 11
Differential Equation Theory	p. 110
Existence and uniqueness of solutions	p. 111
Linear systems of differential equations	p. 112
Stiff differential equations	p. 12
Further Evolutionary Problems	p. 120
Many-body gravitational problems	p. 121
Delay problems and discontinuous solutions	p. 122
Problems evolving on a sphere	p. 123
Further Hamiltonian problems	p. 124
Further differential-algebraic problems	p. 13
Difference Equation Problems	p. 130
Introduction to difference equations	p. 131
A linear problem	p. 132
The Fibonacci difference equation	p. 133
Three quadratic problems	p. 134
Iterative solutions of a polynomial	p. 135
The arithmetic-geometric mean	p. 14
Difference Equation Theory	p. 140
Linear difference equations	p. 141
Constant coefficients	p. 142
Powers of matrices	p. 2
Numerical Differential Equation Methods	p. 20
The Euler Method	p. 200
Introduction to the Euler methods	p. 201
Some numerical experiments	p. 202
Calculations with stepsize control	p. 203
Calculations with mildly stiff problems	p. 204
Calculations with the implicit Euler method	p. 21
Analysis of the Euler Method	p. 210
Formulation of the Euler method	p. 211
Local truncation error	p. 212
Global truncation error	p. 213
Convergence of the Euler method	p. 214
Order of convergence	p. 215
Asymptotic error formula	p. 216
Stability characteristics	p. 217
Local truncation error estimation	p. 218
Rounding error	p. 22
Generalizations of the Euler Method	p. 220
Introduction	p. 221
More computations in a step	p. 222
Greater dependence on previous values	p. 223
Use of higher derivatives	p. 224
Multistep-multistage-multiderivative methods	p. 225
Implicit methods	p. 226
Local error estimates	p. 23
Runge-Kutta Methods	p. 230
Historical introduction	p. 231
Second order methods	p. 232
The coefficient tableau	p. 233
Third order methods	p. 234
Introduction to order conditions	p. 235
Fourth order methods	p. 236
Higher orders	p. 237
Implicit Runge-Kutta methods	p. 238
Stability characteristics	p. 239
Numerical examples	p. 24
Linear Multistep Methods	p. 240
Historical introduction	p. 241
Adams methods	p. 242
General form of linear multistep methods	p. 243
Consistency, stability and convergence	p. 244
Predictor-corrector Adams methods	p. 245
The Milne device	p. 246
Starting methods	p. 247
Numerical examples	p. 25
Taylor Series Methods	p. 250
Introduction to Taylor series methods	p. 251
Manipulation of power series	p. 252
An example of a Taylor series solution	p. 253
Other methods using higher derivatives	p. 254
The use of f derivatives	p. 255
Further numerical examples	p. 26
Hybrid Methods
Table of Contents provided by Publisher. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Numerical Methods for Ordinary Differential Equations

Summary

Table of Contents

Supplemental Materials