Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book.

Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations.

Contents

The basic properties of Richardson extrapolation

Richardson extrapolation for explicit Runge-Kutta methods

Linear multistep and predictor-corrector methods

Richardson extrapolation for some implicit methods

Richardson extrapolation for splitting techniques

Richardson extrapolation for advection problems

Richardson extrapolation for some other problems

General conclusions