A Novel Finite Difference Scheme on Uniform Mesh for Integro-Differential Equations with Small ε-Parameters
International Congress of Mathematicians 2026 (ICM 2026), Pennsylvania, Amerika Birleşik Devletleri, 23 - 30 Temmuz 2026, ss.178-179, (Özet Bildiri)
- Yayın Türü: Bildiri / Özet Bildiri
- Basıldığı Şehir: Pennsylvania
- Basıldığı Ülke: Amerika Birleşik Devletleri
- Sayfa Sayıları: ss.178-179
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Erzincan Binali Yıldırım Üniversitesi Adresli: Evet
Özet
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.