Finite-difference approximation for the u(k)-derivative with O(hM-k+1) accuracy: An analytical expression

Vadim Dubovsky, Alexander Yakhot

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


An approximation of function u(x) as a Taylor series expansion about a point x0 at M points xi, ∼i = 1,2,..., M is used where λi, are arbitrary-spaced. This approximation is a linear system for the derivatives u(λ) with an arbitrary accuracy. An analytical expression for the inverse matrix A-1 where A = [Aik] = 1/k!(xi - x0) k is found. A finite-difference approximation of derivatives u (k) of a given function u(x) at point x0 is derived in terms of the values w(xi).

Original languageEnglish
Pages (from-to)1070-1079
Number of pages10
JournalNumerical Methods for Partial Differential Equations
Issue number5
StatePublished - 1 Jan 2006


  • Accuracy
  • Derivatives
  • Finite-difference approximation
  • General analytical expression
  • Inverse matrix
  • Taylor series


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