The Time Accuracy Analysis of Crank-Nicolson Predictor-Corrector Numerical Scheme for Diffusion Equations

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The Crank-Nicolson is an excellent method for numerically solving some partial differential equations with a finite difference method. Crank-Nicolson Predictor-corrector (CNPC) is proved an efficacious way for numerically solving linear equations. This paper analyzes the time accuracy of CNPC for diffusion equations. In “A predictor-corrector algorithm for reaction-diffusion equations associated with neural activity on branched structures”, the authors claim that the achieved time accuracy of their CNPC correspond with one of the second order. Our exhaustive analysis and tests prove that the time accuracy of the CNPC is worse than the second order accuracy for diffusion equations.
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Explicit Implicit; Domain Decomposition; Diffusion Equation; Accuracy

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M.J. Rempe and D.L. Chopp, A predictor-corrector algorithm for reaction-diffusion equations associated with neural activity on branched structures, SIAM J. Sci. Comput., Vol.28, pp.2139-2161,2006.

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