Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method

Abstract

In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, $\epsilon$. These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.