HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.3, pp.787-799, 2022 (SCI-Expanded)
Article / Article
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
Keywords, difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, Shishkin mesh, Volterra integro-differential equation, COLLOCATION METHOD, DECOMPOSITION METHOD
Van Yüzüncü Yıl University Affiliated:
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.