ABSTRACT
We consider a linear singularly perturbed Volterra integro-differential equation. Our aim is to design and analyse a finite difference method which is robust with respect to the perturbation parameter to solve this equation. The method we construct is a combination of backward Euler difference operator for the differential part and repeated quadrature rules for the integral part. We show that the method is the first-order convergent in the maximum norm. Numerical experiments are carried out on some test examples, confirming the robustness of the proposed scheme.
Disclosure statement
No potential conflict of interest was reported by the authors.