Numerical Schemes Based on Splines for Two-Dimensional Singularly Perturbed Elliptic Partial Differential Equations With Mixed Shifts

In this study, we considered a singular perturbation problem of two-dimensional, linear elliptic partial differential equations having both positive and negative shifts in both directions of the reaction terms, whose solution exhibits characteristic boundary layers. The shift terms are approximated using a Taylor series, and the resultant elliptic equation is treated with a fitted operator spline in tension and a fitted operator spline in compression on a uniform mesh to establish uniform estimates. The effect of the positive and negative shift on the behavior of the solution is explained by executing numerical experiments on three test problems.