Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space

Singularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For time derivative, we use fractional implicit Euler method, followed by fitted finite difference method bilinear interpolation for locally one-dimensional problems. The proposed is shown to be almost first-order convergent spatial direction temporal direction. Theoretical results illustrated numerical examples.