INCREASING THE ORDER OF THE SMF METHOD FOR A SPECIAL TYPE OF PROBLEM.

The SMF method is a numerical code specially designed to integrate perturbed oscillators. The explicit SMF method of n steps has order n + 1 when calculating the solution and order n when calculating the derivative of the solution. For the special case in which the perturbation does not depend on the derivative of the solution it is possible to increase the order of the computation of the derivative by introducing the implicit formula without increasing the number of evaluations. [ABSTRACT FROM AUTHOR]