FITTED NON-POLYNOMIAL SPLINE METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL DIFFERENCE EQUATIONS WITH INTEGRAL BOUNDARY CONDITION

FITTED NON-POLYNOMIAL SPLINE METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL DIFFERENCE EQUATIONS WITH INTEGRAL BOUNDARY CONDITION

H. G. Debela, G. F. Duressa

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Abstract

The aim of this paper is to present  tted non-polynomial spline method for singularly perturbed di erential-di erence equations with integral boundary condition. The stability and uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experi- mentation and solved for di erent values of the perturbation parameter, " and mesh size, h. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and uniformly convergent for h   " where the classical numerical methods fails to give good result and it also improves the results of the methods existing in the literature.

Keywords

Singularly perturbed problems, Delay di erential equation, Non-polynomial spline, Integral boundary condition.