Overlapping Schwarz wave form relaxation for the solution of coupled and decoupled system of convection diffusion reaction equation

In this article we study the convergence and the error bound for the solution of the convection diffusion reaction equation using overlapping Schwarz wave form relaxation method combined with the first order fractional splitting method (Strang's splitting) as basic solver. We extended the study to solve decoupled and coupled system of equations of same class in order to demonstrate the effect of the coupling in the system, through the reaction term, on the convergence and error decay. The accuracy and the efficiency of the methods are investigated through the solution of different model problems of scalar, coupled and decoupled systems of convection diffusion reaction equations.