Interval Schemes for Singularly Perturbed Initial Value Problems

摘要

The modified exponential interval schemes are introduced for the solution of singularly perturbed initial value problems. We give the outline of constructing the schemes of k-th order, then we construct four schemes for k = 1 and k = 2. These schemes are uniformly convergent of second and third order accuracy. Also, we introduce the idea of optimal convergence. Numerical results and comparisons with other schemes are presented.