A fitted operator numerical method for singularly perturbed Fredholm integro-differential equation with integral initial condition
Aklilu Fufa Oljira1, Mesfin Mekuria Woldaregay2
1Department of Mathematics, College of Natural and Computational Science, Oda Bultum University, Chiro, Ethiopia.
Objectives:
In this paper, a uniformly convergent numerical scheme is proposed for solving a singularly perturbed Fredholm integro-differential equation with an integral initial condition. The equation involves a left boundary layer which makes it difficult to solve it using the standard numerical methods. A fitted operator finite difference method is used to approximate the differential part of the equation and the composite Simpson [Formula: see text] rule is used for the integral parts of the equation and the initial condition.
Result:
The stability bound and error estimation of the approximated solution are performed, to show the uniform convergence of the scheme with order one in the maximum norm. Numerical test examples are provided to calculate the maximum absolute errors, thrgence, and the uniform error for a couple of examples to support theoretical analysis.
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