Improving the performance of a code for solving stiff systems of ODEs (Q1122327)

As a part of the solution process LSODE, a widely used code for solving stiff systems of ordinary differential equations, the Jacobian of f must be evaluated which usually requires at least N additional evaluations of f. This can be a dominant cost in backward differentiation formula codes. It is shown that significant improvements to the LSODE code are possible if a copy of the Jacobian is saved and reused. Two different strategies are proposed: the first one evaluates Jacobians at predicted solutions and the second one evaluates Jacobians at accepted solutions. Both strategies are tested on problems from a stiff test set and the performance of both strategies is about the same.