On stable integration of stiff ordinary differential equations with global error control

Authors:
Gennady Yur'evich Kulikov;Sergey Konstantinovich Shindin
Affiliations:
School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa;School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

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Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

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Abstract

In the paper we design an adaptive numerical method to solve stiff ordinary differential equations with any reasonable accuracy set by the user. It is a two-step second order method possessing the A-stability property on any nonuniform grid [3]. This method is also implemented with the local-global step size control developed earlier in [8] to construct the appropriate grid automatically. It is shown that we are able to extend our technique for computation of higher derivatives of fixed-coefficient multistep methods to variable-coefficient multistep methods. We test the new algorithm on problems with exact solutions and stiff problems as well, in order to confirm its performance.