用Haar小波配点法处理具有时滞和位移的奇摄动微分方程

IF 0.7 Q2 MATHEMATICS

Tamkang Journal of Mathematics Pub Date : 2021-02-21 DOI:10.5556/J.TKJM.53.2022.3250

Akmal Raza, Arshad Khan

{"title":"用Haar小波配点法处理具有时滞和位移的奇摄动微分方程","authors":"Akmal Raza, Arshad Khan","doi":"10.5556/J.TKJM.53.2022.3250","DOIUrl":null,"url":null,"abstract":"An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11, 29].","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method\",\"authors\":\"Akmal Raza, Arshad Khan\",\"doi\":\"10.5556/J.TKJM.53.2022.3250\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11, 29].\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/J.TKJM.53.2022.3250\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/J.TKJM.53.2022.3250","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

提出了一种有效的Haar小波配点法，用于求解具有时滞和位移的奇摄动微分方程的数值解。利用泰勒级数(上一阶)将具有时滞和移位的问题转化为不具有时滞和移位的新问题，然后用Haar小波搭配法求解，减少了系统的时间和复杂度。在此基础上，我们直接采用Haar小波配置方法来解决这些问题。此外，我们还通过几个测试实例来展示Haar小波配置方法的准确性和效率，并将我们的结果与有限差分法和拟合算子有限差分法进行了比较[11,29]。

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

Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method

An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11, 29].

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

Tamkang Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

期刊介绍： To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.