An Explicit Single-Step Multi-Jacobian Method for non Stiff Ordinary Differential Equations

A new method for the computation of non stiff systems of ordinary differential equations is described. The method is explicit, single-step, and uses Jacobians evaluated at previous steps, as well as the current step. Second, third and fourth order processes, with error estimators, have been derived and tested. They use only one function evaluation and one Jacobian evaluation per step. The method combines the computational efficiency of the multistep methods with the ease of implementation of the single step methods, especially as regards step control