A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

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

References

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