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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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Keywords: Explicit Runge-Kutta schemes, initial value problem, singularity of the first kind, convergence
Article copyright: © Copyright 1985 American Mathematical Society