Weighted Optimal Formulas for Approximate Integration

Author:

Shadimetov Kholmat12ORCID,Jalolov Ikrom1

Affiliation:

1. Department of Informatics and Computer Graphics, Tashkent State Transport University, 1 Odilkhodjayev Str., Tashkent 100167, Uzbekistan

2. Computational Mathematics Laboratory, V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9 University Str., Tashkent 100174, Uzbekistan

Abstract

Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the current work, we consider a discrete analogue of the differential operator 1−12π2d2dx2m in the Hilbert space H2μR, called Dmβ. We modify the Sobolev algorithm to construct optimal quadrature formulas using a discrete operator. We provide a weighted optimal quadrature formula, using this algorithm for the case where m=1. Finally, we construct an optimal quadrature formula in the Hilbert space H2μR for the weight functions px=1 and px=e2πiωx when m=1.

Publisher

MDPI AG

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