Simple and compact finite difference formulae using real and complex variables
by Yohei Nishidate
International Journal of Computational Science and Engineering (IJCSE), Vol. 26, No. 6, 2023

Abstract: A new set of compact finite difference formulae is derived by simple combinations of the real and the complex Taylor series expansions. The truncation error is fourth-order in derived formulae for approximating first to fourth-order derivatives. Although there exist complex stencil finite difference formulae with better truncation errors, our formulae are computationally cheaper, requiring only three points for first to third-order and four points for fourth-order derivatives. The derived formulae are experimented with for approximating derivatives of relatively simple and highly nonlinear functions used in other literature. Although the new formulae suffer the subtractive cancellation, it is demonstrated that the derived formulae outperform finite difference formulae of comparable computational costs for relatively large step sizes.

Online publication date: Mon, 04-Dec-2023

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