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.

Keywords:

• Stiff initial-value problems
• Uniform schemes
• Higher order schemes

Acknowledgement

The authors are indebted to Professor S. E. El-Gendi for various valuable suggestions and constructive criticism.