Analytical underpinnings of a hybrid analytic-numeric scheme for the Abe-Thurner generalization of the diffusion equation

Abstract

A hybrid analytic-numeric scheme for obtaining approximate solutions to a generalization of the diffusion equation for non-homogenouse media recently introduced by Abe and Thurner [Physica A 356, 403 (2005)] is proposed. The analytical underpinnings of the proposed scheme for evolving a system governed by the one-dimensioanl Abe-Thurner equations starting from general intial conditions are presented. The scheme is applied to the evolution of a Dirac-delta initial distribution. The final result is an expression amenable to numerical integration for the the evolution of the distribution function of a system governed by Abe-Thurner generalized diffusion .