{"title":"求解四阶Sturm-Liouville问题特征值的Chebyshev搭配法","authors":"R. Darzi, B. Agheli","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.15.62","DOIUrl":null,"url":null,"abstract":"In this work, we have suggested that the Chebyshev collocation method can be employed for detecting the eigenvalues of fourth-order Sturm-Liouville problems. Two examples are presented subsequently. Numerical eventuates indicate that the present method is accurate. Introduction The boundary value problems for ordinary differential equations have a notable role theoretically. Also, they have diverse applications. A great number of physical, biological and chemical phenomena, can be explained through using boundary value problems. In this paper, Chebyshev collocationmethod is used to acquire the solutions for the subsequent fourth order nonsingular Sturm-Liouville problems (q0(x)y ′′(x))′′ + (q1(x)y ′(x))′ + (μv(x)− q2(x))y(x) = 0, a < x < b, (1) or y = F (y(x), y′(x), y′′(x), y′′′(x), μ) (2) or y + p3(x)y ′′′(x) + p2(x)y ′′(x) + p1(x)y ′(x) + (μw(x)− r(x))y(x) = 0 (3) with the four linearly independent homogeneous boundary conditions","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"128 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Chebyshev Collocation Method for Finding the Eigenvalues of Fourth-Order Sturm-Liouville Problems\",\"authors\":\"R. Darzi, B. Agheli\",\"doi\":\"10.18052/WWW.SCIPRESS.COM/BMSA.15.62\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we have suggested that the Chebyshev collocation method can be employed for detecting the eigenvalues of fourth-order Sturm-Liouville problems. Two examples are presented subsequently. Numerical eventuates indicate that the present method is accurate. Introduction The boundary value problems for ordinary differential equations have a notable role theoretically. Also, they have diverse applications. A great number of physical, biological and chemical phenomena, can be explained through using boundary value problems. In this paper, Chebyshev collocationmethod is used to acquire the solutions for the subsequent fourth order nonsingular Sturm-Liouville problems (q0(x)y ′′(x))′′ + (q1(x)y ′(x))′ + (μv(x)− q2(x))y(x) = 0, a < x < b, (1) or y = F (y(x), y′(x), y′′(x), y′′′(x), μ) (2) or y + p3(x)y ′′′(x) + p2(x)y ′′(x) + p1(x)y ′(x) + (μw(x)− r(x))y(x) = 0 (3) with the four linearly independent homogeneous boundary conditions\",\"PeriodicalId\":252632,\"journal\":{\"name\":\"Bulletin of Mathematical Sciences and Applications\",\"volume\":\"128 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of Mathematical Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.15.62\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Mathematical Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.15.62","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
在这项工作中,我们提出了Chebyshev配置法可以用于检测四阶Sturm-Liouville问题的特征值。随后给出了两个例子。数值结果表明,该方法是准确的。常微分方程边值问题具有重要的理论意义。此外,它们有各种各样的应用。许多物理、生物和化学现象都可以用边值问题来解释。本文利用Chebyshev配位法,得到了具有四个线性无关齐次边界条件的后续四阶非奇异Sturm-Liouville问题(q0(x)y ' ' (x)) + (q1(x)y ' (x)) + (μv(x) - q2(x))y(x) = 0, a < x < b,(1)或y = F (y(x), y ' (x), y ' (x), y ' (x), y ' (x), μ)(2)或y + p3(x)y ' ' (x) + p2(x)y ' (x) + p1(x)y ' (x) + (μw(x) - r(x))y(x) = 0(3)的解
The Chebyshev Collocation Method for Finding the Eigenvalues of Fourth-Order Sturm-Liouville Problems
In this work, we have suggested that the Chebyshev collocation method can be employed for detecting the eigenvalues of fourth-order Sturm-Liouville problems. Two examples are presented subsequently. Numerical eventuates indicate that the present method is accurate. Introduction The boundary value problems for ordinary differential equations have a notable role theoretically. Also, they have diverse applications. A great number of physical, biological and chemical phenomena, can be explained through using boundary value problems. In this paper, Chebyshev collocationmethod is used to acquire the solutions for the subsequent fourth order nonsingular Sturm-Liouville problems (q0(x)y ′′(x))′′ + (q1(x)y ′(x))′ + (μv(x)− q2(x))y(x) = 0, a < x < b, (1) or y = F (y(x), y′(x), y′′(x), y′′′(x), μ) (2) or y + p3(x)y ′′′(x) + p2(x)y ′′(x) + p1(x)y ′(x) + (μw(x)− r(x))y(x) = 0 (3) with the four linearly independent homogeneous boundary conditions