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Hogeme, Mohammed Sumebo; Woldaregay, Mesfin Mekuria; Rathour, Laxmi; Mishra, Vishnu Narayan

A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method. (English) Zbl 1531.65282

J. Comput. Appl. Math. 441, Article ID 115709, 10 p. (2024).
Summary: This paper implemented a stable numerical scheme for solving singularly perturbed linear second-order Fredholm integro-differential equation. A parameter-uniform numerical method was constructed using an exponentially fitted finite difference method to approximate the differential part and the composite Simpson 1/3 rule for the integral part of the equation. The scheme’s stability and convergence analysis has been carried out. The maximum absolute errors and the rate of convergence are tabulated for different values of the perturbation parameter \(\varepsilon\) and mesh sizes using different numerical test examples.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45B05 Fredholm integral equations
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

Keywords:

singularly perturbed; integro-differential equation; stable numerical method; exponentially fitted scheme; convergence analysis; stability analysis
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References:

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