This research focuses on studying a specific problem involving a second-order delay differential equation that has a discontinuous source term over the interval 0, 2 with an integral boundary condition. The discontinuity is expected to happen at a point d (0, 2), while a tiny positive parameter adjusts the leading coefficient. The solution displays boundary layers at x = 0 and x = 2, and there may be interior layers at x = 1, x = d, and x = 1 + d, depending on the location of d. To tackle this issue, a finite difference method is implemented on a segmented Shishkin mesh. We establish first-order uniform convergence of the scheme with respect to the perturbation parameter, supported by numerical validation.
Elango et al. (Fri,) studied this question.