✦ LIBER ✦
Finite-difference approximation for the u(k)-derivative with O(hM−k+1) accuracy: An analytical expression
✍ Scribed by Vadim Dubovsky; Alexander Yakhot
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 105 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0749-159X
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✦ Synopsis
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 x~i~ are arbitrary‐spaced. This approximation is a linear system for the derivatives u^(k)^ with an arbitrary accuracy. An analytical expression for the inverse matrix A^−1^ where A = [A~ik~] = ${1\over k!}$(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 u(x~i~). © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006