Pseudospectral vs. Finite Difference Methods for Initial Value Problems with Discontinuous Coefficient

An initial value problem with piecewise constant coefficients is considered. The accuracies for both finite difference methods and the pseudospectral method are analyzed, and a modification of the initial value problem is suggested. The modified problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method at integral multiples of the temporal period. Key Words, pseudospectral, finite difference, initial value problem AMS subject classifications. 65M06, 65M70