Absolutely stable fitted mesh scheme for singularly perturbed parabolic convection diffusion equations

In this article, an absolutely stable difference scheme is investigated for solving singularly perturbed time dependent convection–diffusion equations. Problems that exhibit right boundary layer of the working interval boundary layer are considered. Using deviating argument, the original second order singular perturbation problem is transformed into a first order delay differential equation. The uniqueness and stability analysis of the present method are addressed, proving the scheme is absolutely stable. To demonstrate and verify the applicability of the present method, two problems with right boundary layers are considered. The numerical findings shows that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singularly perturbed problems.