A numerical method for an inhomogeneous nonlinear diffusion problem

摘要

A numerical method for the solution of an inhomogeneous nonlinear diffusion problem that arises in a variety of applications is presented. The diffusion coefficient in the underlying diffusion process is concentration- as well as distance- dependent. We wish to determine the concentration of the diffusing substance in a semi-infinite domain at any time, starting with a given initial concentration. The method of solution begins by first mapping the semi-infinite physical domain to a finite computational domain. An implicit finite-difference marching procedure is then used to advance the solution in time. Numerical results are presented for several physical problems. We observe that the present numerical solutions are in good agreement with the analytical solutions obtained previously by other researchers.