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Home  >  volume 36 (no1)

On the Accuracy of Crank Nicolson Method for the Numerical Solutions of Advection – Diffusion Equation by Ayodele Ojo (Pages 55-64)
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Abstract

This paper examined the accuracy of Crank Nicolson method for  approximating the advection – diffusion equation in one-dimension. The method was used to develop a numerical scheme for a given parabolic partial differential equation. The mesh discretization of the numerical scheme resulted into a system of tridiagonal matrices equations which was solved by Thomas algorithm. However, the approximate solutions of  the two numerical examples considered using this method had good agreement with the exact solutions. Thus, Crank Nicolson method has been proven to be order two in space, implicit in time, robust, unconditionally stable and has higher degree of accuracy.

                Keywords: Advection, Diffusion,  Stability, Crank Nicolson Method, Discretization, Exact Solution

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