On The Generation for Numerical Solution of Singularly Perturbed Problem with Right Boundary Layer

Abstract

In this study, we propose an important numerical method for the numerical solution of singularly perturbed convection-diffusion five points boundary value problem using nonuniform mesh. First, we give the some behaviours of the exact solution and its first derivative. We establish finite difference scheme, which is based on interpolating quadrature rules. Then, we prove the convergence of difference scheme and it is uniformly convergent in $ \varepsilon $ perturbation parameter. Furthermore, by a numerical experiment, we demonstrate the efficiency of the proposed method.

Keywords

• Singular perturbation
• finite difference scheme
• nonuniform mesh
• uniformly convergence
• five point boundary condition
• discrete maximum norm

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