A numerical solution for unsteady anisotropic diffusion reaction equation of time–space variable coefficients

Abstract

Two-dimensional transient problems for anisotropic functionally graded materials governed by a diffusion reaction 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 boundary element method for the solutions. These boundary element method solutions are then numerically inverse transformed to get the solutions in the time variable. Some problems of trigonometrically, exponentially and quadratically graded materials are solved. The numerical solutions obtained are quite accurate.