The Asymptotic Solution of Differential Equations with a Turning Point and Singularities PDF Download
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Author: R. C. Thorne
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 22
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Author: R. C. Thorne
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 22
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Author: Wolfgang Wasow
Publisher: Springer Science & Business Media
ISBN: 1461210909
Category : Mathematics
Languages : en
Pages : 255
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Book Description
My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization.
Author: R. C. Thorne
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 140
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Author: Rudolph Ernest Langer
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 44
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Author: Wolfgang Wasow
Publisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385
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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.
Author: R. B. White
Publisher: World Scientific
ISBN: 1848166087
Category : Mathematics
Languages : en
Pages : 430
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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.
Author: Tadepalli Ventata Subrahmanya Lakshmi Narasimnha Sastry
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 158
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Author: Keldibay Alymkulov
Publisher:
ISBN:
Category : Technology
Languages : en
Pages :
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Book Description
Here, we generalize the boundary layer functions method (or composite asymptotic expansion) for bisingular perturbed differential equations (BPDE that is perturbed differential equations with singular point). We will construct a uniform valid asymptotic solution of the singularly perturbed first-order equation with a turning point, for BPDE of the Airy type and for BPDE of the second-order with a regularly singular point, and for the boundary value problem of Cole equation with a weak singularity.A uniform valid expansion of solution of Lighthill model equation by the method of uniformization and the explicit solution-this one by the generalization method of the boundary layer function-is constructed. Furthermore, we construct a uniformly convergent solution of the Lagerstrom model equation by the method of fictitious parameter.
Author: Robert Leonard Evans
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 182
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Author: Wallace Eugene Johnson
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 70
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