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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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: http://dx.doi.org/10.1090/S0025-5718-1985-0771033-0
PII: S 0025-5718(1985)0771033-0
Keywords: Explicit Runge-Kutta schemes, initial value problem, singularity of the first kind, convergence
Article copyright: © Copyright 1985 American Mathematical Society