Numerical solution of singularly perturbed differential difference equations with mixed parameters

Abstract

In this paper, numerical solution of the singularly perturbed differential equations with mixed parameters are considered. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter, $varepsilon$ and mesh size, $h$. The numerical results are tabulated and it is observed that the present method is more accurate and $varepsilon$-uniformly convergent for $hgeqvarepsilon$, where the classical numerical methods fails to give good result.