The application of Runge-Kutta schemes to singular initial value problems

Authors:
Frank de Hoog and Richard Weiss

Journal:
Math. Comp. **44** (1985), 93-103

MSC:
Primary 65L05

MathSciNet review:
771033

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Abstract: A theory for explicit Runge-Kutta schemes applied to the initial value problem for a first-order system of differential equations with a singularity of the first kind is developed. It is shown that, in general, the order of convergence is at most two but that the usual order up to a logarithmic term can be obtained for level three and four schemes applied to specific problems.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771033-0

Keywords:
Explicit Runge-Kutta schemes,
initial value problem,
singularity of the first kind,
convergence

Article copyright:
© Copyright 1985
American Mathematical Society