Abstract
Enright [Numerical Analysis Report 122, University of Manchester, Manchester, U.K., 1986] implements a Runge-Kutta method for solving the initial value problem using an alternative to the standard local error control scheme. The aim is to control the defect associated with a local interpolant by sampling its value at one or more fixed points within each step. However, in general, the quality of a sample point is problem-dependent and also varies from step to step. Two classes of interpolant are presented for which the asymptotic behaviour of the defect is known a priori, allowing optimal sample points to be chosen.
Original language | English |
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Pages (from-to) | 1175-1183 |
Number of pages | 9 |
Journal | Siam journal on numerical analysis |
Volume | 26 |
Issue number | 5 |
Publication status | Published - 1989 |
Keywords / Materials (for Non-textual outputs)
- Runge-Kutta formula
- defect
- interpolation
- numerical mathematics