A difference scheme using a parametric spline for differential difference equation with twin layers

In this study, a parametric spline approach is used to evaluate the solution of differential-difference equations with delay and advanced parameters having twin layers. Using the continuity condition of the first-order derivative of the spline at the interior node, the difference scheme is derived. Thenon-standard finite differences for the first derivatives are employed in the scheme to increase the precision of the solution. According to an analysis of the suggested approach, its fourth-order convergence is established.  Maximum absolute errors for the examples chosen from the literature are tabulated. To demonstrate the effectiveness of the method, numerical results are shown along with comparisons to other methods.

Keywords:

Differential-difference equation , Twin layers , Parametric spline , Maximum error