E-grāmata: Richardson Extrapolation: Practical Aspects and Applications

A powerful and popular numerical procedure, Richardson extrapolation can improve the performance of computer programs that handle large time-dependent scientific and engineering problems, say Zlatev and colleagues, and scientists and engineers often use it in their treatment of advanced large-scale mathematical models of various phenomena. After explaining its basic properties, they describe its use in explicit Runte-Kutta methods, linear multi-step and predictor-corrector methods, some implicit methods, splitting techniques, advection problems, and other problems. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)

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

The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences.