Terminal boundary-value technique for solving singularly perturbeddelay differential equations

Abstract

terminal boundary-value technique is presented for solving singularly perturbed delay differential equations, the solutions ofwhich exhibit layer behaviour. 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 was determined. The outer region problem with the implicit boundarycondition was solved and produces an explicit boundary condition for the inner region problem. Then, the modified inner regionproblem (using the stretching transformation) is solved as a two-point boundary value problem. The second-order finite differencescheme was used to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Tovalidate the efficiency of the method, some model examples were solved. The stability and convergence of the scheme was alsoinvestigated.© 2014 Taibah University. Production and hosting by Elsevier B.V. All rights reserved.MSC: 65L03; 65L10; 65L11; 65L12Keywords: Singular perturbation; Delay differential equations; Finite differences; Terminal boundary condition; Boundary layer1