Local-error estimates for variable-step Runge-Kutta methods
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.
KeywordsLocal Error Integration Step Aberdeen Prove Ground Additional Function Evaluation Typical Integration Time
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