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Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics

Authors: Shalashilin, V.I., Kuznetsov, Evgenii

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  • ISBN 978-94-017-2537-8
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Hardcover $99.99
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Softcover $99.00
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  • ISBN 978-90-481-6391-5
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About this book

A decade has passed since Problems of Nonlinear Deformation, the first book by E.I. Grigoliuk: and V.I. Shalashilin was published. That work gave a systematic account of the parametric continuation method. Ever since, the understanding of this method has sufficiently broadened. Previously this method was considered as a way to construct solution sets of nonlinear problems with a parameter. Now it is c1ear that one parametric continuation algorithm can efficiently work for building up any parametric set. This fact significantly widens its potential applications. A curve is the simplest example of such a set, and it can be used for solving various problems, inc1uding the Cauchy problem for ordinary differential equations (ODE), interpolation and approximation of curves, etc. Research in this area has led to exciting results. The most interesting of such is the understanding and proof of the fact that the length of the arc calculated along this solution curve is the optimal continuation parameter for this solution. We will refer to the continuation solution with the optimal parameter as the best parametrization and in this book we have applied this method to variable c1asses of problems: in chapter 1 to non-linear problems with a parameter, in chapters 2 and 3 to initial value problems for ODE, in particular to stiff problems, in chapters 4 and 5 to differential-algebraic and functional differential equations.

Table of contents (8 chapters)

  • Nonlinear Algebraic or Transcendental Equations with a Parameter

    Shalashilin, V. I. (et al.)

    Pages 1-42

  • The Cauchy Problem for Ordinary Differential Equations

    Shalashilin, V. I. (et al.)

    Pages 43-66

  • Stiff Systems of Ordinary Differential Equations

    Shalashilin, V. I. (et al.)

    Pages 67-95

  • Differential — Algebraic Equations

    Shalashilin, V. I. (et al.)

    Pages 97-135

  • Functional — Differential Equations

    Shalashilin, V. I. (et al.)

    Pages 137-147

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-94-017-2537-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-1-4020-1542-7
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
Softcover $99.00
price for USA in USD
  • ISBN 978-90-481-6391-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics
Authors
Copyright
2003
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-2537-8
DOI
10.1007/978-94-017-2537-8
Hardcover ISBN
978-1-4020-1542-7
Softcover ISBN
978-90-481-6391-5
Edition Number
1
Number of Pages
VIII, 228
Number of Illustrations and Tables
1 b/w illustrations
Topics