Open AccessOn exponential fitting of finite difference methods for heat equations
Author(s) -
E.O. Tuggen,
C. E. Abhulimen
Publication year - 2021
Language(s) - English
DOI - 10.47260/jamb/1211
Subject(s) - mathematics , truncation error , finite difference , truncation (statistics) , finite difference coefficient , finite difference method , exponential function , heat equation , stability (learning theory) , space (punctuation) , dispersion (optics) , mathematical analysis , computer science , finite element method , physics , statistics , mixed finite element method , machine learning , optics , thermodynamics , operating system
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.