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9780898713336

The Boundary Function Method for Singular Perturbation Problems

by ; ;
  • ISBN13:

    9780898713336

  • ISBN10:

    0898713331

  • Format: Hardcover
  • Copyright: 1995-05-01
  • Publisher: Society for Industrial & Applied

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Summary

This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology.

Table of Contents

Basic Ideas
Regular and singular perturbations
Asymptotic approximations
Asymptotic and convergent series
Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems
Singularly perturbed ordinary differential equations
Initial value problem
The critical case
Boundary value problems
Spike-type solutions and other contrast (dissipative) structures
Singularly perturbed partial differential equations
The method of Vishik-Lyusternik
Corner boundary functions
The smoothing procedure
Systems of equations in critical cases
Periodic solutions
Hyperbolic systems
Applied problems
Mathematical model of combustion process in the case of autocatalytic reaction
Heat conduction in thin Bodies
Application of the boundary function method in the theory of semiconductor devices
Relaxation waves in the FitzHugh-Nagumo system
On some other applied problems
Index
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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