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An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral
Muhammet Enes Durmaz1, Ilhame Amirali2, Gabil M Amiraliyev3
1Department of Information Technology, Kırklareli University, Kırklareli, 39100 Turkey.
Abstract:
In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.
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