Mathematics – Numerical Analysis
Scientific paper
2009-02-21
Russian Journal of Mathematical Modelling 19, 6 (2007) 61--70
Mathematics
Numerical Analysis
12 pages
Scientific paper
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an arbitrary approximation of the Jacobian matrix. In opposite to our previous paper, the fourth stage is explicit. So, the constructed method also has a good stability properties because of L-stability of the intermediate numerical formulas in the fourth stage, but has a lower computational costs per step. Automatic stepsize selection based on local error and stability control are performed. The estimations for error and stability control have been obtained without significant additional computational costs. Numerical experiments show reliability and efficiency of the implemented integration algorithm.
Novikov Evgeny
Tuzov Anton
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