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The Boundary Function Method for Singular Perturbation Problems

All titles
The Boundary Function Method for Singular Perturbation Problems

The Boundary Function Method for Singular Perturbation Problems

Adelaida B. Vasil'eva
Valentin F. Butuzov
Leonid V. Kalachev
April 1995
Hardback
9780898713336
£61.00
GBP
Hardback
    Description

    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.

    Product details

    April 1995
    Hardback
    9780898713336
    0 pages
    260 × 183 × 23 mm
    0.738kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    Table of Contents

    • 1. Basic Ideas
    • Regular and singular perturbations
    • Asymptotic approximations
    • Asymptotic and convergent series
    • Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems
    • 2. Singularly perturbed ordinary differential equations
    • Initial value problem
    • The critical case
    • Boundary value problems
    • Spike-type solutions and other contrast (dissipative) structures
    • 3. 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
    • 4. 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.
      • Show more
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    Additional Information
    About the authors
      Authors
    • Adelaida B. Vasil'eva
    • Valentin F. Butuzov
    • Leonid V. Kalachev

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