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
fitting, Finite difference, Local truncation error, Heat equations.