Dirichlet series solution of equations arising in boundary layer theory

The differential equation F′'' + AFF′'+ BF′ 2 = 0, where A and B are arbitrary constants subject to different types of boundary conditions, is considered. This class of equations frequently occurs in boundary-layer theory. The proposed Dirichlet series method, in conjunction with an u...

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Published in	Mathematical and computer modelling Vol. 32; no. 9; pp. 971 - 980
Main Authors	Sachdev, P.L., Bujurke, N.M., Pai, N.P.
Format	Journal Article
Language	English
Published	Oxford Elsevier Ltd 01.11.2000 Elsevier Science
Subjects	Analytic continuation Approximations and expansions Calculus of variations and optimal control Dirichlet Series Euler transformation Exact sciences and technology Mathematical analysis Mathematics Padé approximants Sciences and techniques of general use Unconstrained optimization Dirichlet Series Padé approximants Unconstrained optimization Euler transformation Analytic continuation Transcendental equation Approximation Boundary value problem Fluid dynamics Numerical solution Dirichlet series Padé approximant Euler scheme Partial differential equation Boundary layer
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ISSN	0895-7177 1872-9479
DOI	10.1016/S0895-7177(00)00183-7

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Abstract	The differential equation F′'' + AFF′'+ BF′ 2 = 0, where A and B are arbitrary constants subject to different types of boundary conditions, is considered. This class of equations frequently occurs in boundary-layer theory. The proposed Dirichlet series method, in conjunction with an unconstrained optimization procedure, is found useful in analyzing these problems. The series so generated is analyzed using Euler transformation and Padé approximants.
AbstractList	The differential equation F′'' + AFF′'+ BF′ 2 = 0, where A and B are arbitrary constants subject to different types of boundary conditions, is considered. This class of equations frequently occurs in boundary-layer theory. The proposed Dirichlet series method, in conjunction with an unconstrained optimization procedure, is found useful in analyzing these problems. The series so generated is analyzed using Euler transformation and Padé approximants.
Author	Bujurke, N.M. Pai, N.P. Sachdev, P.L.
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Cites_doi	10.1063/1.864868 10.1017/S0022112064000416 10.1093/qjmam/16.1.1 10.1007/BF01589285 10.1007/BF00042897 10.1080/14786443109461870
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Keywords	Dirichlet Series Padé approximants Unconstrained optimization Euler transformation Analytic continuation Transcendental equation Approximation Boundary value problem Fluid dynamics Numerical solution Dirichlet series Padé approximant Euler scheme Partial differential equation Boundary layer
Language	English
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References_xml	– start-page: 602 year: 1997 end-page: 633 ident: BIB13 article-title: A Compendium on Nonlinear Ordinary Differential Equations – year: 1957 ident: BIB14 article-title: Introduction to Dirichlet Series – volume: 73 start-page: 223 year: 1973 ident: BIB16 publication-title: Proc. Camb. Phil. Soc. – volume: 18 start-page: 31 year: 1984 ident: BIB18 article-title: A note on the solution of a differential equation arising in boundary layer theory publication-title: J. Engg. Mathematics – volume: 33 start-page: 223 year: 1937 ident: BIB3 article-title: On an equation occuring in Falkner and Skan's approximate treatment of the boundary layer publication-title: Proc. Camb. 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Snippet	The differential equation F′'' + AFF′'+ BF′ 2 = 0, where A and B are arbitrary constants subject to different types of boundary conditions, is considered. This...
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SubjectTerms	Analytic continuation Approximations and expansions Calculus of variations and optimal control Dirichlet Series Euler transformation Exact sciences and technology Mathematical analysis Mathematics Padé approximants Sciences and techniques of general use Unconstrained optimization
Title	Dirichlet series solution of equations arising in boundary layer theory
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