Solution of singularly perturbed system of 2D parabolic convection diffusion differential-difference equations using alternating direction method

Modelling of reaction diffusion equation with more than one mass density functions gives the coupled system of partial differential equations. Through the coupling of functions, the behavior of some components of solution may changes by the influence of the other components. These behaviour of the solutions can be studied by solving the coupled system of equations. In this article, we investigate system of singularly perturbed 2D parabolic differential-difference equations. One type of study is the numerical investigation. To start with, first we applied the backward Euler scheme to discretize the temporal derivative, and then we applied a combination of bilinear interpolation and fitted monotone numerical difference method to the locally dimensional reduced 1D differential equations. We have proved that, the fitted monotone method with bilinear interpolation is almost first order convergent in both spatial and temporal directions. To illustrate the theoretical results, numerical test example is provided.