A NumericalInvestigation for a Class of Transient-State Variable Coefficient DCR Equations

In this paper, a combined Laplace transform (LT) and boundary element method (BEM) is used to find numerical solutions to problems of anisotropic functionally graded media that are governed by the transient diffusion–convection–reaction equation. First, the variable coefficient governing equation is reduced to a constant coefficient equation. Then, the Laplace-transformed constant coefficients equation is transformed into a boundary-only integral equation. Using a BEM, the numerical solutions in the frame of the Laplace transform may then be obtained from this integral equation. Then, the solutions are inversely transformed numerically back to the original time variable using the Stehfest formula. The numerical solutions are verified by showing their accuracy and steady state. For symmetric problems, the symmetry of solutions is also justified. Moreover, the effects of the anisotropy and inhomogeneity of the material on the solutions are also shown, to suggest that it is important to take the anisotropy and inhomogeneity into account when performing experimental studies.