Robust computing technique for reaction diffusion 2D parabolic problems with shift

Higher dimensional singularly perturbed problems frequently appears in many mathematical modelling. Solving such higher dimensional problem is not as much easy as possible. So order reducing technique namely alternating direction method is one such good choice for solving them. Further singular perturbation problem has its own complexities like boundary and/or interior layers, hence it requires a fitted method on special mesh. Reaction diffusion type singular perturbation problem with space shift is considered in this article. The presence of space shift leads strong interior layer in the solution. To take care of interior and boundary layers, a special mesh is constructed. Hence the problem considered in this article is solved by alternating direction method and fitted difference method with bilinear interpolation. Further the convergence analysis also carried out with rate one in both time and space. Computational validation is also done.