Point source function for a singularly perturbed difference scheme on a uniform 2D (Q1878721)

The author considers a finite-difference analog of a singularly-perturbed stationary parabolic equation of reaction-diffusion type in the rectangular mesh. The author finds an asymptotic expansion as \(\sqrt{\varepsilon/h}\to0\) for the point source function of this equation different in the cases where \(-1/2<\alpha\leq )\) and \(-1/2<\alpha<2(1+\kappa^2){-1};\) here, \(\varepsilon\) is a small parameter, \(h\) is the step of the mesh, \(\alpha\) is a characteristic of the grid, and \(\kappa\) is the ratio of the steps.