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The Boundary Function Method for Singular Perturbation Problems

The Boundary Function Method for Singular Perturbation Problems

Part of Studies in Applied and Numerical Mathematics

  • Date Published: January 1987
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898713336


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About the Authors
  • 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.

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    Product details

    • Date Published: January 1987
    • format: Hardback
    • isbn: 9780898713336
    • dimensions: 260 x 183 x 23 mm
    • weight: 0.738kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • 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

  • Authors

    Adelaida B. Vasil'eva

    Valentin F. Butuzov

    Leonid V. Kalachev

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