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 : 25 | Download : 9

Publication Date : 2022-06-01

Article Type : Research Paper

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