Local extrapolation in the solution of ordinary differential equations

Author:

Shampine L. F.

Abstract

The local errors being estimated in the solution of an initial value problem can be added in to make the solution more accurate but this is not always advisable. A rule for deciding when to extrapolate is studied for one-step methods. Some observations about the correctness of local error estimators and extrapolation of multistep methods are also made.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference10 articles.

1. Comparing error estimators for Runge-Kutta methods;Shampine, L. F.;Math. Comp.,1971

2. Mathematical Centre Tracts;Zonneveld, J. A.,1964

3. Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme;Fehlberg, E.;Computing (Arch. Elektron. Rechnen),1970

4. Two-step processes by one-step methods of order 3 and of order 4;Shintani, Hisayoshi;J. Sci. Hiroshima Univ. Ser. A-I Math.,1966

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