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Interpolating high-order Runge-Kutta formulas. (English) Zbl 0707.65054
When the solution of an initial value problem in ordinary differential equations is required at certain specified values of the independent variable, the use of Runge-Kutta integration formulae is complicated by the need to either perform interpolation, or to repeatedly restrict step sizes so that the specified points are exactly reached.
The authors present a hybrid approach.
At each stage, their method determines the largest step size for which interpolation will produce errors smaller than the given tolerance, at all points in the span of the step. If the next specified point lies within this span, interpolation is used. Otherwise, it may be possible to step directly to the point by using the integration formula. A method that uses a pair of integration formula of orders 7 and 8, and an interpolation formula of order 5, is constructed and shown to be efficient.
Reviewer: S.Wright

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
Full Text: DOI
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