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Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation. (English) Zbl 1442.65136

Summary: In this paper, we consider the linear first order singularly perturbed Fredholm integro-differential equation. For the solution of this problem, fitted difference scheme is constructed on a Shishkin mesh. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The method is proved to be second-order convergent in the discrete maximum norm. Also, numerical results are given to support theoretical analysis.

MSC:

65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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References:

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