Lagrange Interpolation in Matrix Form for Numerical Differentiation and Integration

Author:

Wang Rui1,Ly Binh-Le2,Xie Wei-Chau1,Pandey Mahesh1

Affiliation:

1. Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Canada

2. Atomic Energy of Canada, Ltd, Mississauga, Canada

Abstract

Numerical differentiation has been widely applied in engineering practice due to its remarkable simplicity in the approximation of derivatives. Existing formulas rely on only three-point interpolation to compute derivatives when dealing with irregular sampling intervals. However, it is widely recognized that employing five-point interpolation yields a more accurate estimation compared to the three-point method. Thus, the objective of this study is to develop formulas for numerical differentiation using more than three sample points, particularly when the intervals are irregular. Based on Lagrange interpolation in matrix form, formulas for numerical differentiation are developed, which are applicable to both regular and irregular intervals and can use any desired number of points. The method can also be extended for numerical integration and for finding the extremum of a function from its samples. Moreover, in the proposed formulas, the target point does not need to be at a sampling point, as long as it is within the sampling domain. Numerical examples are presented to illustrate the accuracy of the proposed method and its engineering applications. It is demonstrated that the proposed method is versatile, easy to implements, efficient, and accurate in performing numerical differentiation and integration, as well as the determination of extremum of a function.

Publisher

Science Publishing Group

Reference16 articles.

1. M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, vol. 55. US Government printing office, 1968.

2. R. Hamming, Numerical methods for scientists and engineers, 2nd Edition. New York: McGraw-Hill, 2012.

3. T. Sauer, Numerical Analysis, 2nd Edition. Addison- Wesley Publishing Company: Pearson, 2011.

4. J. Grabmeier, E. Kaltofen, and V. Weispfenning, Computer algebra handbook: foundations, applications, systems. Berlin: Springer, 2003. https://doi.org/10.1007/978-3-642-55826-9

5. S. Wolfram, The Mathematica Book, 4th Edition. Cambridge: Cambridge university press, 1999.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3