An accelerated technique for the coupled system of reaction-diffusion-transport equations arising from catalytic converters

Abstract

A study on accelerated monotone iterative methods for two systems of non-linear partial differential equations arising from catalytic converter models is presented. Two mathematical models are considered in this work. The first mathematical model consists of a semilinear parabolic partial differential equation and two integral equations. In contrast, the second mathematical model consists of a semilinear parabolic partial differential equation and an integral equation. The proposed modified monotone iterative methods converge to the unique solution of these mathematical models faster than the existing monotone iterative schemes available in the literature. Interesting theoretical justification is provided for the accelerated convergence and the monotone behaviour of the proposed iterative methods. Numerical simulation results support the theoretical claims.