Preface
Flowchart of contents
I Ordinary differential equations 1
1 Euler's method and beyond 3
2 Multistep methods 19
3 Runge-Kutta methods 33
4 Stiff equations 53
5 Error control 73
6 Nonlinear algebraic systems 91
II The Poisson equation 103
7 Finite differences schemes 105
8 The finite element method 135
9 Gaussian elimination for sparse linear equations 169
10 Iterative methods for sparse linear equations 185
11 Multigrid techniques 227
12 Fast Poisson solvers 245
III Partial differential equations of evolution 267
13 The diffusion equation 269
14 Hyperbolic equations 307
Appendix: Bluffer's guide to useful mathematics 347
Index 367