Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 97, Issue 4, Pages 759-771Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2019.1585828
Keywords
Singularly perturbed problems; Volterra integro-differential equation; boundary layer; finite difference scheme; uniform convergence; error bound
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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.
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