A priori and a posteriori error analysis for a system of singularly perturbed Volterra integro-differential equations

In this work, we consider a system of Volterra integro-differential equations with initial conditions. The derivative term in equations is multiplied with distinct small positive parameters giving rise to overlapping layers. We propose a numerical scheme that avoids the extra condition on the problem's data required by the scheme of Liang et al. (Comput Appl Math 39:255, 2020). We derive a priori and a posteriori error bounds for the proposed scheme and further rectify the shortcomings of a posteriori error estimation in Liang et al. (Comput Appl Math 39:255, 2020). Numerical results are presented in the form of graphs and tables that validate the proposed theory.

Automated summary

In this work, a system of Volterra integro-differential equations with initial conditions is considered. The derivative term in the equations is multiplied by distinct small positive parameters, leading to overlapping layers. A numerical scheme is proposed that avoids the extra condition on the problem's data required by a previous scheme. A priori and a posteriori error bounds for the proposed scheme are derived, and shortcomings in the a posteriori error estimation of the previous scheme are rectified. Numerical results in the form of graphs and tables are presented to validate the proposed theory.