Application of a New Method of Discretization to Diffusion-Reaction Problems

Abstract

This paper presents a new integral solution method known as the Green Element Method (GEM). The technique of this solution, which relies essentially on the singular integral theory of the Boundary Element Method (BEM), is applied to problems involving mass diffusion and reaction in one dimension. This procedure employs the fundamental solution of the term with the highest derivative to construct a system of equations where both the dependent variable and its gradient become the primary variables. A linear weighting function in spatial dimensions is employed to approximate the scalar variables over the problem domain. The resulting banded coefficient matrix can be handled efficiently by matrix subroutines. Numerical results from test problems involving both linear and nonlinear reaction kinetics and different time discretization schemes show that this method is reliable and can produce accurate results.