Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

  • Authors:

  • I. R. Khan;R. Ohba;N. Hozumi

  • Affiliations:

  • -;-;-

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2003

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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.