Malaysian Journal of Mathematical Sciences, September 2019, Vol. 13, No. 3
A Mathematical Proof of Explicit Formulas for the Coefficients of Finite Difference Approximations of Second Derivatives
Syafwan, H., Sutra, Y. Y., Alkhairi, R., Syafwan, M., Ramdhan, W., and Yusda, R. A.
Corresponding Email: mahdhivan@sci.unand.ac.id
Received date: 6 November 2018
Accepted date: 16 August 2019
Abstract:
Explicit formulas for the coefficients of finite difference approximations of first and higher derivatives in any order of accuracy have been presented by Khan and Ohba. They also have provided a mathematical proof of the formulas for first derivatives. In this paper, the proof is extended for second derivatives. The proof is constructed based on Taylor series, and employs some properties of Vandermonde determinant which are not found in the proof for first derivatives.
Keywords: Finite difference approximations, Taylor series, Vandermonde matrix, determinant
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