Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition

Authors: MUHAMMET ENES DURMAZ, GABİL AMİRALİ, MUSTAFA KUDU

Abstract: In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.

Keywords: Fredholm integro differential equation, singular perturbation, finite difference methods, Shishkin mesh, uniform convergence

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