A Numerical technique for solving a class of semilinear singularly perturbed boundary value problems

Abstract

In this work, we have studied a numerical scheme based on Sinc collocation method to solve a class of semilinear singularly perturbed  boundary value problems. The solution of the problems exhibit a boundary layer on the both
    sides or one side of the domain due to the presence of perturbation parameter $\epsilon$. The Sinc method  can control  the oscillations in computed solutions at boundary layer regions naturally because the distribution of Sinc points is denser at near the boundaries. The convergence analysis is discussed and the method is shown to be an exponential
convergent. The numerical results support the theoretical results and illustrate the efficiency and accuracy  of the method compared with the results in the existing methods.