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Mathematical proof of closed form expressions for finite difference approximations based on Taylor series |
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| Authors: | Ishtiaq Rasool Khan Ryoji Ohba Noriyuki Hozumi |
| Institution: | a Department of Information and Media Sciences, The University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu 808-0135, Japan b Collaboration Center, Kitakyushu Foundation for the Advancement of Industry, Science and Technology, 2-1 Hibikino, Wakamatsu-ku, Kitakyushu 808-0135, Japan c Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan |
| Abstract: | Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series. |
| Keywords: | Finite difference approximations Forward difference approximations Backward difference approximations Central difference approximations Taylor series Numerical differentiation |
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