Uniform convergence analysis of the BDF2 scheme on Bakhvalov-type meshes for a singularly perturbed Volterra integro-differential equation

A singularly perturbed Volterra integro-differential problem is considered. At first, this problem is discretized by using the variable two-step backward differentiation formula (BDF2) and the trapezoidal formula on a Bakhvalov-type mesh to approximate the first-order derivative term and the integral term, respectively. Then, the stability and convergence analysis of the proposed numerical method are carried out. It is shown that the proposed numerical method is second-order uniformly convergent with respect to perturbation parameter ɛ in the discrete maximum norm. Finally, the theoretical find is illustrated by numerical experiments.