A second order optimal hybrid scheme for singularly perturbed semilinear parabolic problems with interior layers

Abstract

An improved time-accurate hybrid finite difference scheme is studied for singularly perturbed semilinear parabolic problems with interior layers. After dealing with the semilinearity through Newton's linearization technique, the temporal direction is treated by the implicit Euler scheme. The space derivatives are handled with a hybrid scheme on two- layer resolving meshes namely, the Shishkin mesh and the Bakhvalov-Shishkin mesh. Richardson extrapolation is applied in time to get rid of the reduction of the order of accuracy outside the layer region. The robustness of the scheme is proved through two test examples among which one is the time-delayed model.