Almost second order finite difference method for singularly perturbed delay differential equations

Abstract

In this thesis, we consider singularly perturbed differential equation containing delay parameter on the convection and reaction terms. The considered problem exhibits left or right boundary layer, depending on the sign of the coefficient of convection term. The terms with delay treated using Taylor’s series approximation. The resulting asymptotically equivalent singularly perturbed boundary value problem is solved using the technique of fitted mesh finite difference method. The stability and consistency of the scheme is investigated to guarantee the convergence of the scheme. Further, the theoretical finding is validated using numerical examples that confirm the betterment of the present method than some existing method in the literature.