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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Kulikov, G. Y. eich, & Shindin, S. K. (2005). On stable integration of stiff ordinary differential equations with global error control. In Lecture Notes in Computer Science (Vol. 3514, pp. 41–49). Springer Verlag. https://doi.org/10.1007/11428831_6
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