Optimal extended one-step schemes of exponential type for stiff initial-value problems

Abstract

Extended one-step schemes of exponential type are introduced for the numerical solution of stiff initial-value problems. These schemes are uniformly convergent of third and fourth orders of accuracy. In addition, we show that these schemes are optimal when ε → 0. Numerical results and comparisons with other schemes are presented.

Numerical Solution of Singularly Perturbed BVPs using an Optimal Fitted One-Step Integration Scheme via Initial Value Method

“…Discretizing SPIVP (9) by the Exponentially Fitted One-Step Scheme (EFFD) derived by Salama and Bakr [15] results in the following optimal fitted one-step integration scheme…”

“…Proof. See Salama and Bakr [15], and Doolan et al [2] Theorem 3. Let () yx be the solution of SPBVP (1) and j w be the numerical solution obtained by the two-term recurrence relation (17).…”