Journal of Applied Mathematics & Bioinformatics

On exponential fitting of finite difference methods for heat equations

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• Abstract

  In this article, a new kind of finite difference scheme that is exponentially fitted, inspired from Fourier analysis, for a fourth space derivative was developed for solving diffusion problems. Dispersion relation and local truncation error of the method were discussed. Stability analysis of the method revealed that it is conditionally stable. Compared to the corresponding fourth order classical scheme in the literature, the proposed scheme is efficient and accurate.

  Mathematics Subject Classification (2020): 65M06, 65N06.

  Keywords: Exponential fitting, Finite difference, Local truncation error, Heat equations.