A numerical investigation of unsteady space-time dependent coefficients anisotropic-diffusion convection reaction equation

Two dimensional transient problems for anisotropic FGMs governed by a diffusion convection reaction (DCR) equation of time-space dependent coefficients are considered. Using a transformation, the space-time dependent coefficients equation is reduced to a time dependent coefficients equation. Then taking a Laplace transform will result in a constant coefficients equation which can be written in forms of boundary-only integral equations and solved using a standard BEM for the solutions. These BEM solutions are then numerically inverse transformed to get the solutions in the time variable. Some problems of trigonometrically, exponentially and quadratically graded materials with compressible or incompressible flow are solved. The numerical solutions obtained are quite accurate.