- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 3
- A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equation...
A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh
Authors : Musa Çakir, Baransel Güneş
Pages : 787-799
Doi:10.15672/hujms.950075
View : 12 | Download : 3
Publication Date : 2022-06-01
Article Type : Research
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.Keywords : difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, Shishkin mesh, Volterra integro-differential equation