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Asymptotic and Computational Analysis最新文献

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Uniform Asymptotic Remainders 一致渐近余数
Asymptotic and Computational Analysis Pub Date : 2020-12-17 DOI: 10.1201/9781003072584-11
D. S. Jones
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引用次数: 0
Approximating Zeros of Solutions of Second-Order Linear ODEs by “Phase Function” Methods 二阶线性微分方程解的“相函数”逼近
Asymptotic and Computational Analysis Pub Date : 2020-12-17 DOI: 10.1201/9781003072584-39
R. Spigler, M. Vianello
{"title":"Approximating Zeros of Solutions of Second-Order Linear ODEs by “Phase Function” Methods","authors":"R. Spigler, M. Vianello","doi":"10.1201/9781003072584-39","DOIUrl":"https://doi.org/10.1201/9781003072584-39","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133471956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Asymptotic Methods in Magnetoconvection 磁对流中的渐近方法
Asymptotic and Computational Analysis Pub Date : 2020-12-17 DOI: 10.1201/9781003072584-36
N. Rudraiah
{"title":"Asymptotic Methods in Magnetoconvection","authors":"N. Rudraiah","doi":"10.1201/9781003072584-36","DOIUrl":"https://doi.org/10.1201/9781003072584-36","url":null,"abstract":"The effects of Lorentz force and non-uniform temperature gradient on the onset of magnetoconvection in an electrically conducting horizontal Boussinesq fluid layer permeated by a uniform transverse magnetic field are studied analytically using linear stability analysis by specifying constant temperature or constant heat flux at the boundaries. It is shown that when the Chandrasekhar number Q → ∞ the correct asymptotic value of the critical Rayleigh number, Rc, can be obtained from the non-viscous MHD equations using a single-term Galerkin expansion. The criterion for the onset of magnetoconvection is determined using a regular perturbation technique with wave-number as perturbation parameter. The method of matched asymptotics is used to predict explicitly the effect of the Hartmann boundary layer (that exists at the rigid boundary for large values of Q) on the onset of magnetoconvection. It is shown that the effect of the Hartmann boundary layer is to increase the asymptotic value of Rc by an amount proportional to the value of the Hartmann number M. We find that the ratios Rci/Rcl where Rci (i = 1 to 6) are the asymptotic values of RC for different nonlinear temperature profiles, are independent of Q but dependent on thermal depth e. It is also shown that the power law for asymptotic values of Rci depends crucially on the nature of heating and not on the nature of the boundaries.","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125567202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Polynomial Asymptotic Estimates of Gegenbauer, Laguerre, and Jacobi Polynomials Gegenbauer、Laguerre和Jacobi多项式的多项式渐近估计
Asymptotic and Computational Analysis Pub Date : 2020-12-17 DOI: 10.1201/9781003072584-22
N. Temme
{"title":"Polynomial Asymptotic Estimates of Gegenbauer, Laguerre, and Jacobi Polynomials","authors":"N. Temme","doi":"10.1201/9781003072584-22","DOIUrl":"https://doi.org/10.1201/9781003072584-22","url":null,"abstract":"We discuss asymptotic forms of CJ( x ), L~( x), P~0t,/3) ( x ), the Gegenbauer, Laguerre and Jacobi polynomials. The asymptotic behavior of these classical orthogonal polynomials has been the subject of several investigations. The research usually concentrates on the case that the degree n of the polynomial is the large parameter, and for all classical orthogonal polynomials the asymptotic behavior is well established now. Inside the domain of the zeros of the polynomial the behavior can be described in terms of elementary functions, such as trigonometric functions. In the domain where the transition from oscillatory to monotonic behavior occurs, familiar higher transcendental functions can be used as estimates. For example, the \"first\" zeros of the Jacobi polynomial can be approximated in terms of the zeros of the J Bessel function. In SzEGO ( 1958) several classical results can be found. For Jacobi polynomials he gives an estimate of","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128605218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Asymptotics of Pearcey’s Integral for Complex Variables 复变量Pearcey积分的渐近性
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-35
R. Paris
{"title":"The Asymptotics of Pearcey’s Integral for Complex Variables","authors":"R. Paris","doi":"10.1201/9781003072584-35","DOIUrl":"https://doi.org/10.1201/9781003072584-35","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117048187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Generalization of Olver’s Algorithm for Linear Difference Systems 线性差分系统中Olver算法的推广
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-26
R. V. Zahar
{"title":"A Generalization of Olver’s Algorithm for Linear Difference Systems","authors":"R. V. Zahar","doi":"10.1201/9781003072584-26","DOIUrl":"https://doi.org/10.1201/9781003072584-26","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130318727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graphs as an Aid to Understanding Special Functions 图形作为理解特殊函数的辅助工具
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-2
R. Askey
{"title":"Graphs as an Aid to Understanding Special Functions","authors":"R. Askey","doi":"10.1201/9781003072584-2","DOIUrl":"https://doi.org/10.1201/9781003072584-2","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131079501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Continental Shelf Wave Scattering: Partial Removal of the Rigid Lid 大陆架波散射:刚性盖的部分去除
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-28
A. Davis
{"title":"Continental Shelf Wave Scattering: Partial Removal of the Rigid Lid","authors":"A. Davis","doi":"10.1201/9781003072584-28","DOIUrl":"https://doi.org/10.1201/9781003072584-28","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125390689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Eigenvalues with Exponentially Small Imaginary Part 关于虚部指数小的特征值
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-41
A. Wood, R. Paris
{"title":"On Eigenvalues with Exponentially Small Imaginary Part","authors":"A. Wood, R. Paris","doi":"10.1201/9781003072584-41","DOIUrl":"https://doi.org/10.1201/9781003072584-41","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121598417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-Order Differential Equations: The Simple Pole Case 二阶线性微分方程系数函数的渐近展开式:简单极点情况
Asymptotic and Computational Analysis Pub Date : 2020-12-11 DOI: 10.1201/9781003072584-4
W. Boyd
{"title":"Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-Order Differential Equations: The Simple Pole Case","authors":"W. Boyd","doi":"10.1201/9781003072584-4","DOIUrl":"https://doi.org/10.1201/9781003072584-4","url":null,"abstract":"","PeriodicalId":394750,"journal":{"name":"Asymptotic and Computational Analysis","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114356543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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