Numerical Treatment of Uniformly Convergent Method for Convection Diffusion Problem

Abstract

In this paper, we will study the convergence properties of the method designed for the convection-diffusion problem. We will prove that the analytical and numerical methods give the same result. Merging the ideas in previous research, we introduce a numerical algorithm on a uniform mesh that requires no exact solution to the local convection-diffusion problem. We display how to obtain the numerical solution of the local Boundary Value Problem (BVP) in a suitable way to ensure that the resulting numerical algorithm recaptures the same convergence properties when using the exact solution of the local BVP. We prove that the proposed algorithm nodally converges to the exact solution.

Keywords

• Trapezoidal rule
• convection-diffusion problem
• boundary value problem
• singular points
• Green’s function
• Lagrange interpolation.

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