Layer resolving numerical scheme for singularly perturbed parabolic convection-diffusion problem with an interior layer

Singularly perturbed parabolic convection-diffusion problem with interior layer is a type of singularly perturbed boundary value problems which have sign change properties in the coefficient function of the convection term. This paper introduces a layer resolving numerical scheme for solving the numerical solution of the singularly perturbed parabolic convection-diffusion problem exhibiting interior layer due to the convection coefficient. The scheme is formulated by discretizing the temporal variable on uniform mesh and discretize the spatial one on piecewise uniform mesh of the Shishkin mesh type. The resulting scheme is shown to be almost first order convergent. Theoretical investigations are confirmed by numerical experiments. Moreover, the present scheme is: • Stable, • Consistent and • Gives more accurate solution than existing methods in the literature.