A uniformly convergent numerical method for singularly perturbed semilinear integro-differential equations with two integral boundary conditions. (English) Zbl 1534.65270
Summary: This paper purposes to present a new discrete scheme for the singularly perturbed semilinear Volterra-Fredholm integro-differential equation including two integral boundary conditions. Initially, some analytical properties of the solution are given. Then, using the composite numerical integration formulas and implicit difference rules, the finite difference scheme is established on a uniform mesh. Error approximations for the approximate solution and stability bounds are investigated in the discrete maximum norm. Finally, a numerical example is solved to show \(\varepsilon \)-uniform convergence of the suggested difference scheme.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
Keywords:
discrete scheme; error bounds; integral boundary condition; integro-differential equation; singular perturbationReferences:
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