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

Lecture Notes in Computer Science, 3514 (2005), 42-49
http://dx.doi.org/10.1007/11428831_6

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.