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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- © Copyright 1985 American Mathematical Society
- Journal: Math. Comp. 44 (1985), 93-103
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1985-0771033-0
- MathSciNet review: 771033