A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations
This paper presents a <i>ε</i>-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/19/3560 |
| Summary: | This paper presents a <i>ε</i>-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. An error analysis is successfully carried out on the Boglaev–Bakhvalov-type mesh. Some numerical experiments are included to authenticate the theoretical findings. In this regard, the main advantage of the suggested method is to yield stable results on layer-adapted meshes. |
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| ISSN: | 2227-7390 |