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Solving singularly perturbed differential-difference equations with dual layer using exponentially fitted spline method

In this paper, we presented exponentially fitted spline method to solve SPDDE with dual layer. At first, the given second order differential-difference equation is replaced by an asymptotically proportionate second order singular perturbation problem. At that point, a fitting factor is brought into the exponentially fitted spline Method. The value of fitting factor is obtained by the singular perturbations theory. The Thomas algorithm is used to solve the tridiagonal system obtained by the method. The result of the delay and also advance parameters on the boundary layer(s) has likewise been evaluated as well as represented in charts. The applicability of the proposed plan is actually confirmed through executing it on model examples. To show the accuracy of the method, the results are presented in terms of maximum absolute errors for arbitrary λ1, λ2 such that λ1 +λ2 =1/2.