menu

Composite Asymptotic Expansions
by Augustin Fruchard and Reinhard Schafke




Overview -
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.

  Read Full Product Description
 
local_shippingFor Delivery
In Stock.
This item is Non-Returnable.
FREE Shipping for Club Members help
 
storeBuy Online Pickup At Store
search store by zipcode

 
 
New & Used Marketplace 11 copies from $43.36
 
 
 

More About Composite Asymptotic Expansions by Augustin Fruchard; Reinhard Schafke

 
 
 

Overview

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.


This item is Non-Returnable.

 

Details

  • ISBN-13: 9783642340345
  • ISBN-10: 3642340342
  • Publisher: Springer
  • Publish Date: December 2012
  • Page Count: 161
  • Dimensions: 9.21 x 6.14 x 0.38 inches
  • Shipping Weight: 0.56 pounds

Series: Lecture Notes in Mathematics #2066

Related Categories

 

BAM Customer Reviews