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Local-error estimates for variable-step Runge-Kutta methods

  • A. Prothero
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 109)

Abstract

Estimates of the local errors arising in the solution of initial-value problems by Runge-Kutta methods may be obtained without additional computation by considering two or more integration steps together. For a given Runge-Kutta method, the parameters occurring in the local-error formula must satisfy a given set of linear equations. General solutions for second-, third- and fourth-order Runge-Kutta methods are given. Typical integration times for a variable-step fourth-order Runge-Kutta method incorporating such an error estimate are 30% shorter than those for the same method using the well-known step-halving estimates.

Keywords

Local Error Integration Step Aberdeen Prove Ground Additional Function Evaluation Typical Integration Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • A. Prothero

There are no affiliations available

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