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A polyvalent Runge-Kutta triple. (English) Zbl 0818.65066
A Runge-Kutta triple is derived consisting of a main formula of order 7, a formula of order 5 for local error estimation and a continuous extension formula of order 5. A family of such triples depending on 6 parameters is considered. The criteria used in selecting the method include accuracy and stability of the main formula and measures of the quality of the local error estimate and the continuous extension. Testing against comparable methods is reported for some delay equations and for the DETEST set of problems.

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems
65L70 Error bounds for numerical methods for ordinary differential equations
34K05 General theory of functional-differential equations
Full Text: DOI
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