The use of higher order finite difference schemes is not dangerous

被引：8
|
作者：
Mathe, Peter [1 ]
Pereverzev, Sergei V. [2 ]
机构：
[1] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany
[2] Johann Radon Inst RICAM, A-4040 Linz, Austria
来源：
JOURNAL OF COMPLEXITY | 2009年 / 25卷 / 01期
关键词：
Numerical differentiation; Finite difference scheme; Spline approximation; NUMERICAL DIFFERENTIATION;
D O I：
10.1016/j.jco.2008.05.007
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We discuss the issue of choosing a finite difference scheme for numerical differentiation in case the smoothness of the underlying function is unknown. If low order finite difference schemes are used for smooth functions, then the best possible accuracy cannot be obtained. This call be circumvented by using higher order finite difference schemes, but there is concern that this may cause bad error behavior. Here we show, theoretically and by numerical simulation, that this is not the case. However, by doing so, the step-size should be chosen a posteriori. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：3 / 10
页数：8
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