Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems

Abstract

A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.