A fitted method for singularly perturbed differential-difference equations having boundary layers via deviating argument and interpolation

Abstract

In this paper, singularly perturbed differential-difference equation having boundary layers at one end (left or right) is considered. In order to obtain numerical solution to these problems, the given second order equation having boundary layer is converted into a singularly perturbed ordinary differential equation using Taylor’s transformation afterwards the resultant singularly perturbed ordinary differential equation is replaced by an asymptotically equivalent to first order differential equation with a small deviating argument. Resulting first order differential equation, is solved by choosing the proper integrating factor (fitting factor) and linear interpolation formulas. The numerical results for several test examples demonstrate the applicability of the method.