A Novel Finite Difference Scheme on Uniform Mesh for Integro-Differential Equations with Small ε-Parameters
International Congress of Mathematicians 2026 (ICM 2026), Pennsylvania, United States Of America, 23 - 30 July 2026, pp.178-179, (Summary Text)
- Publication Type: Conference Paper / Summary Text
- City: Pennsylvania
- Country: United States Of America
- Page Numbers: pp.178-179
- Open Archive Collection: AVESIS Open Access Collection
- Erzincan Binali Yildirim University Affiliated: Yes
Abstract
This study presents a computational method of the first order for solving Volterra–Fredholm integro-differential equations with boundary layers. A numerical finite difference scheme is constructed on a uniform mesh. This is achieved by using the composite right-sided rectangle formula for the integral part, and interpolating quadrature rules and linear exponential basis functions for the differential part. It is demonstrated that the numerical scheme achieves first-order accuracy and uniformly converges with respect to the small ε-parameter. The efficacy of this approach is demonstrated by examining the performance of the numerical scheme in a single example.