A First Course in the Numerical Analysis of Differential Equations

✍ Scribed by Arieh Iserles

• Publisher: Cambridge University Press
• Year: 1996
• Tongue: English
• Leaves: 393
• Series: Cambridge texts in applied mathematics
• Category: Library

✦ Synopsis

This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; and methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.

✦ Table of Contents

cover......Page 1
A First Course in the Numerical Analysis of Differential Equations......Page 2
Contents......Page 4
Preface......Page 8
Flowchart of contents......Page 14
PART I Ordinary differential equations......Page 16
1 Euler's method and beyond......Page 18
2 Multistep methods......Page 34
3 Runge-Kutta methods......Page 48
4 Stiff equations......Page 68
5 Error control......Page 88
6 Nonlinear algebraic systems......Page 106
PART II The Poisson equation......Page 118
7 Finite digerence schemes......Page 120
8 The finite element method......Page 150
9 Gaussian elimination for sparse linear equations......Page 184
10 Iterative methods for sparse linear equations......Page 200
11 Multigrid techniques......Page 242
12 Fast Poisson solvers......Page 260
PART III Partial dinerential equations of evolution......Page 282
13 The digusion equation......Page 284
14 Hyperbolic equations......Page 322
Appendix Bluner's guide to useful mathematics......Page 362
A.1 Linear algebra......Page 363
A.2 Analysis......Page 374
Index......Page 382