A Novel Fitted Three Term Method for the Numerical Treatment of Singularly Perturbed Differential–Difference Equations

An exponentially fitted method is proposed on uniform mesh for the numerical treatment of a boundary-value problem for the singularly perturbed differential–difference equations of second order with both the positive and negative small shifts. An approximate version of the problem is constructed first and then, a fitted tridiagonal scheme is derived using the Hermite interpolation and exponential fitting factor. ’Thomas Algorithm’ is used to solve the resulting system of equations. Applicability of the method is validated by comparing the results. The effect of shifts on the solutions is investigated and presented in figures.