Abstract
In this paper, the reliability of the two methods from the family of fourth-order implicit finite difference schemes, namely the fourth-order Crank-Nicolson approximation scheme and the fourth-order standard implicit approximation scheme in solving the diffusion equation has been studied. The corresponding system of linear approximation equations for both fourth-order schemes were derived and then solved iteratively. In addition, for the purpose of assessing the efficiency of both schemes, comparison was made by considering three parameters, which are the iteration numbers, the computation time and the maximum error. Based on the results of the numerical experiments, it shows that the performance of the fourth-order Crank-Nicolson scheme is more efficient compared to the fourth-order standard implicit scheme in solving one-dimensional (1D) diffusion equation.
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