Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
Book Description
Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Asymptotic Expansions of Solutions of Differential Linear Equations of the Second Order in a Complex Domain
Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
Book Description
Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
Book Description
Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Author:
Publisher: Elsevier
ISBN: 0080871291
Category : Mathematics
Languages : en
Pages : 307
Book Description
Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Publisher: Elsevier
ISBN: 0080871291
Category : Mathematics
Languages : en
Pages : 307
Book Description
Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Asymptotic Expansions for Ordinary Differential Equations
Author: Wolfgang Wasow
Publisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385
Book Description
This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Publisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385
Book Description
This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Composite Asymptotic Expansions
Author: Augustin Fruchard
Publisher: Springer
ISBN: 3642340350
Category : Mathematics
Languages : en
Pages : 169
Book Description
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Publisher: Springer
ISBN: 3642340350
Category : Mathematics
Languages : en
Pages : 169
Book Description
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Asymptotic Analysis
Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 384
Book Description
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 384
Book Description
Asymptotic Expansions: The asymptotic behaviour of the real solutions of certain second order differential equations
Author: Johannes Gualtherus van der Corput
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 356
Book Description
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 356
Book Description
Asymptotic Analysis of Differential Equations
Author: R. B. White
Publisher: World Scientific
ISBN: 1848166087
Category : Mathematics
Languages : en
Pages : 430
Book Description
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Publisher: World Scientific
ISBN: 1848166087
Category : Mathematics
Languages : en
Pages : 430
Book Description
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
The asymptotic solution of linear second order differential equations in a domain containing a turning point and regular singularity
Author: R. C. Thorne
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 140
Book Description
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 140
Book Description
Asymptotics and Special Functions
Author: F. W. J. Olver
Publisher: Academic Press
ISBN: 148326744X
Category : Mathematics
Languages : en
Pages : 589
Book Description
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Publisher: Academic Press
ISBN: 148326744X
Category : Mathematics
Languages : en
Pages : 589
Book Description
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Expansions in Series of Solutions of Linear Difference-Differential and Infinite Order Differential Equations with Constant Coefficients
Author: Douglas G. Dickson
Publisher: American Mathematical Soc.
ISBN: 0821812238
Category : Asymptotic expansions
Languages : en
Pages : 78
Book Description
Publisher: American Mathematical Soc.
ISBN: 0821812238
Category : Asymptotic expansions
Languages : en
Pages : 78
Book Description