On stable integration of stiff ordinary differential equations with global error control
Kulikov, Gennady Yu; Shindin, S.K.
Lecture Notes in Computer Science, 3514 (2005), 42-49
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 . This method is also implemented with the local-global step size control developed earlier in  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.