## Abstract

An approximation of function u(x) as a Taylor series expansion about a point x_{0} at M points x_{i}, ∼i = 1,2,..., M is used where λ_{i}, 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 = [A_{ik}] = 1/k^{!}(x_{i} - x_{0}) ^{k} is found. A finite-difference approximation of derivatives u ^{(k)} of a given function u(x) at point x_{0} is derived in terms of the values w(x_{i}).

Original language | English |
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Pages (from-to) | 1070-1079 |

Number of pages | 10 |

Journal | Numerical Methods for Partial Differential Equations |

Volume | 22 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 2006 |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

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