Abstract:
In this paper, a domain decomposition method has been presented for solving singularly perturbed
differential difference equations with delay as well as advances whose solution exhibits boundary layer behavior.
By introducing a terminal point, the original problem is divided into inner and outer region problems. An implicit
terminal boundary condition at the terminal point has been determined. The outer region problem with the implicit
boundary condition is solved and produces an explicit boundary condition for the inner region problem. Then, the
modified inner region problem (using the stretching transformation) is solved as a two-point boundary value
problem. Fourth order stable central difference method has been used to solve both the inner and outer region
problems. The proposed method is iterative on the terminal point. To demonstrate the applicability of the method,
some numerical examples have been solved for different values of the perturbation parameter, delay and advance
parameters. The stability and convergence of the scheme has also investigated.