A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.3, pp.787-799, 2022 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 51 Issue: 3
- Publication Date: 2022
- Doi Number: 10.15672/hujms.950075
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.787-799
- Keywords: Keywords, difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, Shishkin mesh, Volterra integro-differential equation, COLLOCATION METHOD, DECOMPOSITION METHOD
- Open Archive Collection: AVESIS Open Access Collection
- Van Yüzüncü Yıl University Affiliated: Yes
Abstract
In this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh. The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.