A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra-Fredholm Integro-Differential Equations
MATHEMATICS, cilt.10, sa.19, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Derleme
- Cilt numarası: 10 Sayı: 19
- Basım Tarihi: 2022
- Doi Numarası: 10.3390/math10193560
- Dergi Adı: MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Anahtar Kelimeler: error analysis, finite difference method, Fredholm integro-differential equation, singular perturbation, Volterra integro-differential equation, uniform convergence, CONVERGENCE ANALYSIS, NUMERICAL-METHOD, SYSTEM
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
This paper presents a epsilon-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.