用正弦余弦小波展开逼近二阶导数有界的函数及其应用

Poincare Journal of Analysis and Applications Pub Date : 2023-06-30 DOI:10.46753/pjaa.2023.v010i01.014

Vivek Kumar Sharma, Virendra Sharma, S. Lal, H. Srivastava, R. .

{"title":"用正弦余弦小波展开逼近二阶导数有界的函数及其应用","authors":"Vivek Kumar Sharma, Virendra Sharma, S. Lal, H. Srivastava, R. .","doi":"10.46753/pjaa.2023.v010i01.014","DOIUrl":null,"url":null,"abstract":". In this paper, sine-cosine wavelet has been introduced and the approximation errors of the function f ( t ) whose first and second derivatives are bounded have been estimated using this wavelet and it is used to solve some linear differential equations. Solution obtained by this method is compared with Euler’s method and with exact solution. We observe that the solution obtained by this method is better than the solution given by the Euler’s method which shows the usefulness of this method.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"APPROXIMATION OF A FUNCTION HAVING BOUNDED DERIVATIVES UPTO THE SECOND ORDER BY SINE-COSINE WAVELET EXPANSION AND ITS APPLICATIONS\",\"authors\":\"Vivek Kumar Sharma, Virendra Sharma, S. Lal, H. Srivastava, R. .\",\"doi\":\"10.46753/pjaa.2023.v010i01.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, sine-cosine wavelet has been introduced and the approximation errors of the function f ( t ) whose first and second derivatives are bounded have been estimated using this wavelet and it is used to solve some linear differential equations. Solution obtained by this method is compared with Euler’s method and with exact solution. We observe that the solution obtained by this method is better than the solution given by the Euler’s method which shows the usefulness of this method.\",\"PeriodicalId\":37079,\"journal\":{\"name\":\"Poincare Journal of Analysis and Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Poincare Journal of Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46753/pjaa.2023.v010i01.014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Poincare Journal of Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46753/pjaa.2023.v010i01.014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

．本文引入了正弦余弦小波，利用该小波估计了一阶导数和二阶导数有界的函数f (t)的逼近误差，并将其用于求解一些线性微分方程。并与欧拉法和精确解进行了比较。我们观察到，用这种方法得到的解比用欧拉法得到的解要好，说明了这种方法的实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

APPROXIMATION OF A FUNCTION HAVING BOUNDED DERIVATIVES UPTO THE SECOND ORDER BY SINE-COSINE WAVELET EXPANSION AND ITS APPLICATIONS

. In this paper, sine-cosine wavelet has been introduced and the approximation errors of the function f ( t ) whose first and second derivatives are bounded have been estimated using this wavelet and it is used to solve some linear differential equations. Solution obtained by this method is compared with Euler’s method and with exact solution. We observe that the solution obtained by this method is better than the solution given by the Euler’s method which shows the usefulness of this method.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Poincare Journal of Analysis and Applications Mathematics-Applied Mathematics

CiteScore

0.60

自引率

0.00%

发文量