On Green's function methods to solve nonlinear reaction-diffusion systems
Recent studies have shown that the usage of classical discretization techniques (e.g., orthogonal collocation, finite-differences, etc.) for reaction-diffusion models cannot be stable in a wide range of parameter values as required, for instance, in model parameter estimation. Oriented to reduce the adverse effects of numerical differentiation, integral equation formulations based on Green's function methods have been considered, in the chemical engineering fields. In this paper, a further exploration of this approach for nonlinear reaction-diffusion transport is carried out. To this end, the Green's function problem is presented and solved for three geometries (i.e., rectangular, cylindrical and spherical), and three representative examples are worked out to illustrate the ability of the method to describe accurately the phenomena with respect to analytical and numerical solutions via finite-differences. Our results show that: (i) by avoiding numerical differentiation, the round-off error propagation is significantly reduced, (ii) boundary conditions are exactly incorporated without approximation order reduction and (iii) more accurate calculations are performed making use of less mesh points and computer time. (C) 2007 Elsevier Ltd. All rights reserved.
green's function reaction-diffusion iterative solution finite-differences effectiveness factor