Numerical solutions of a system of singularly perturbed reaction-diffusion problems

Abstract

This paper addresses the numerical approximation of solutions to  a
coupled system of singularly perturbed reaction-diffusion
equations. The components of the solution
 exhibit overlapping boundary and interior layers. The Sinc-Galerkin method is used to solve
 these problems, Sinc procedure  can control  the
oscillations in computed solutions at boundary layer regions
naturally because the distribution of Sinc points is denser at
near the boundaries. Also the obtained results show that the proposed method  is applicable even for small
 perturbation parameter as $\epsilon=2^{-30}$. The convergence analysis
 of proposed technique is discussed, it is shown
that the approximate solutions converge to the exact solutions at
an  exponential rate. Numerical experiments are carried out to
demonstrate the accuracy and efficiency of the method.