Exponentially fitted finite difference methods for a singularly perturbed nonlinear differential-difference equation with a small negative shift

Abstract

This study presents exponentially fitted finite difference methods for solving a singularly perturbed nonlinear differential-difference equation that consists of a small negative shift. The quasilinearization technique is applied to the nonlinear problem and a sequence of linear problems is obtained. The resulting linear problems are treated with exponentially fitted finite difference methods of higher order. The methods developed in this paper are studied for stability and convergence. Numerical results using the proposed methods are presented for two test problems and hence the efficiency of the methods is demonstrated.