DOMAIN DECOMPOSITION METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL DIFFERENCE EQUATIONS WITH LAYER BEHAVIOR

Authors : Gemechis File Duressa, Y N Reddy

Pages : 86-102

Doi:10.24107/ijeas.251236

View : 102 | Download : 9

Publication Date : 2015-03-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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
Keywords : Singular perturbation, Differential difference equations, Finite Differences, Terminal Boundary Condition, Boundary layer

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