AUTHORS: Lakshmi Sireesha Ch.

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ABSTRACT: In this paper, a non standard finite difference method, with reference to the solution of a class of singularly perturbed singular boundary value problems on a uniform mesh, is discussed. The non-polynomial spline forms the tool for the solution of the problem. The discretized equation of the problem is developed using the condition of continuity for the first order derivatives of the non polynomial spline, at the interior nodes and it is not valid at the singularity. Hence, at the singularity, the boundary value problem is modified in order to get a three term relation. The tridiagonal scheme of the method is processed using discrete invariant imbedding algorithm. The convergence of the method is analyzed and maximum absolute errors in the solution are tabulated. Root mean square errors in the solution of the examples are presented in comparison with the methods chosen from the literature, to establish the proposed method.

KEYWORDS: Singularly perturbed two point singular boundary value problem, Interior nodes, Singular point, Non-polynomial spline, Boundary layer

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