Hybrid Numerical/Analytical Approach to Nonlinear Diffusion Problems

A class of nonlinear diffusion-type problems is handled through a hybrid method. This method incorporates the ideas in the generalized integral transform technique to reduce the original partial differential equation into a denumerable system of coupled ordinary differential equations. These equations can then be solved through standard numerical techniques, once the system is truncated to a finite order. Sufficient conditions for the convergence of the truncated finite system are then examined. An application is considered that deals with a transient radiative fin problem, which is quite suitable for illustrating the solution methodology and convergence behavior.