[For the first edition (1988) see Zbl 0657.65003).]
This book provides an introduction into the numerical solution of ordinary and partial differential equations. It concentrates on practical aspects of the presented methods and algorithms, while theoretical aspects (like e. g. convergence analysis) stay much more in the background. Nevertheless, the analytic basis of the investigated differential equation problems, as well as some physical origins, are explained in all chapters. Many FORTRAN 90 programs are integrated into the text which lead, together with many exercises, the reader directly to practical applications.
After some introduction into linear algebraic system solvers, initial value problems for ordinary differential equations are treated by explicit and implicit one-step and multistep methods, followed by line methods for parabolic initial value problems, and hyperbolic transport and wave equations. The next two chapters are devoted to stationary problems; the first of these deals with finite differences, the second with finite element methods. In Appendix A the author reports on his own work on the general package PDE2D of programs for solving a wide range of differential equation problems numerically.