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Finite Difference Method for Nonlocal Singularly Perturbed Problem

Journal: International Journal of Modern Research in Engineering and Technology (Vol.1, No. 5)

Publication Date:

Authors : ;

Page : 25-39

Keywords : Singular perturbation; finite difference method; Bakhvalov mesh; nonlocal boundary condition; uniform convergence.;

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In this study, nonlinear singularly perturbed problems with nonlocal condition are evaluated by finite difference method. The exact solution ????(????) has boundary layers at ???? = 0 and ???? = 1. We present some properties of the exact solution of the multi-point boundary value problem (1)-(3). According to the perturbation parameter, by the method of integral identities with the use exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form uniformly convergent finite difference scheme on Bakhvalov mesh is established. The error analysis for the difference scheme is performed. ???? − uniform convergence for approximate solution in the discrete maximum norm is provided, which is the firstorder (O(h)). This theoretical process is applied on the sample. By Thomas Algorithm, it has been shown to be consistent with the theoretical results of numerical results. The results were embodied in table and graphs. The relationship between the approximate solution with the exact solution are obtained by Maple 10 computer program.

Last modified: 2018-08-25 16:57:28