eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-10-12 2 5 336 343 10.12691/ajams-2-5-7 AJAMS2014257 article Lakshmi Sirisha 1 Y.N. Reddy ynreddy_nitw@yahoo.com 1 Department of Mathematics, National Institute of Technology, WARANGAL, INDIA In this paper, we discuss the numerical solution of singularly perturbed differential-difference equations exhibiting dual layer behavior. First the second order singularly perturbed differential-difference equation is replaced by an asymptotically equivalent second order singularly perturbed ordinary differential equation. Then, second order stable central difference scheme has been applied to get a three term recurrence relation which is easily solved by Discrete Invariant Imbedding Algorithm. Some numerical examples have been considered to validate the computational efficiency of the proposed numerical scheme. To analyze the effect of the parameters on the solutions, the numerical solutions have also been plotted using graphs. The error bound and convergence of the method have also been established. http://pubs.sciepub.com/ajams/2/5/7/ajams-2-5-7.pdf singular perturbations differential-difference equations dual layer delay parameter advance parameter