Efficient Extrapolation Methods for ODEs, II
Open Access
- 1 January 1985
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 5 (1) , 23-28
- https://doi.org/10.1093/imanum/5.1.23
Abstract
Extrapolation methods for the solution of the initial-value problem for a system of ordinary differential equations (ODEs) advance the integration one step by combining the results of a number of subintegrations carried out with a simple method and fixed step size. The choice of step size in the subintegrations influences the efficiency of the resulting formula. In a first investigation it was shown how to quantify this influence. Here this influence is studied when the code is attempting to select the optimal order at each step. A novel result about this optimal order allows the two most important experimental developments to be fully explained.Keywords
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