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An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

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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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Durmaz, M.E., Amirali, I. & Amiraliyev, G.M. An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition. J. Appl. Math. Comput. 69, 505–528 (2023). https://doi.org/10.1007/s12190-022-01757-4

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