A class of exponential methods for stiff initial-value problems

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