Composite Asymptotic Expansions

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Composite Asymptotic Expansions by Augustin Fruchard, Reinhard Schafke, Springer Berlin Heidelberg
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Augustin Fruchard, Reinhard Schafke ISBN: 9783642340352
Publisher: Springer Berlin Heidelberg Publication: December 15, 2012
Imprint: Springer Language: English
Author: Augustin Fruchard, Reinhard Schafke
ISBN: 9783642340352
Publisher: Springer Berlin Heidelberg
Publication: December 15, 2012
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Berlin Heidelberg

Cover of the book Low Dimensional Semiconductor Structures by Augustin Fruchard, Reinhard Schafke
Cover of the book Neocortical Grafting to Newborn and Adult Rats: Developmental, Anatomical and Functional Aspects by Augustin Fruchard, Reinhard Schafke
Cover of the book Computer Vision, Imaging and Computer Graphics: Theory and Applications by Augustin Fruchard, Reinhard Schafke
Cover of the book Antibody Engineering Volume 1 by Augustin Fruchard, Reinhard Schafke
Cover of the book Aesthetic Surgery of the Breast by Augustin Fruchard, Reinhard Schafke
Cover of the book Metal-Organic Frameworks for Photonics Applications by Augustin Fruchard, Reinhard Schafke
Cover of the book Springer Handbook of Lasers and Optics by Augustin Fruchard, Reinhard Schafke
Cover of the book Tumours I. Organic Diseases by Augustin Fruchard, Reinhard Schafke
Cover of the book Novel Selenium-Mediated Rearrangements and Cyclisations by Augustin Fruchard, Reinhard Schafke
Cover of the book Gradually-varied Flow Profiles in Open Channels by Augustin Fruchard, Reinhard Schafke
Cover of the book Nuclear Reactions by Augustin Fruchard, Reinhard Schafke
Cover of the book Evidence-Based Practice in Complementary and Alternative Medicine by Augustin Fruchard, Reinhard Schafke
Cover of the book Integrated Business Information Systems by Augustin Fruchard, Reinhard Schafke
Cover of the book Optimierung by Augustin Fruchard, Reinhard Schafke
Cover of the book Dental Pathology by Augustin Fruchard, Reinhard Schafke
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy