A CLASS OF EXPONENTIAL METHODS FOR STIFF INITIAL-VALUE PROBLEMS

In this paper, we derive a class of exponential methods for solving th e stiff initial-value problems. The present methods are unconditionall y stable and satisfy a discrete maximum principle. These include an ev en order of accuracy when the perturbation parameter, epsilon, is fixe d and have the property that if epsilon is of order h they reduce to f irst order accuracy. Also, these methods are optimal when epsilon --> 0. Finally, good results and comparison with the uniform second-order scheme are considered.