Springer Series in Computational Mathematics

Numerical Methods for Nonlinear Partial Differential Equations

Authors: Bartels, Sören

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  • Provides rigorous numerical analyses for the treatment of modern applications with state-of-the-art approximation schemes
  • Includes explanations of the mathematical modeling and analytical properties for the problems considered
  • Simple Matlab codes allow the reader to test the numerical methods in two- and three-dimensional situations
  • First book on the numerical analysis of nonlinear partial differential equations
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eBook $99.00
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  • ISBN 978-3-319-13797-1
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Hardcover $119.99
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Softcover $129.00
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  • ISBN 978-3-319-35680-8
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  • Usually dispatched within 3 to 5 business days.
About this book

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Reviews

“This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. … The target audience of the book is postgraduates and experienced researchers. … this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations.” (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016)

“This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. … This book presents a very nice transition from graduate-level material to state-of-the-art research topics. … This is a nice and well-written advanced textbook.” (Karsten Urban, Mathematical Reviews, October, 2015)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-319-13797-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-13796-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • ISBN 978-3-319-35680-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Methods for Nonlinear Partial Differential Equations
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
47
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-13797-1
DOI
10.1007/978-3-319-13797-1
Hardcover ISBN
978-3-319-13796-4
Softcover ISBN
978-3-319-35680-8
Series ISSN
0179-3632
Edition Number
1
Number of Pages
X, 393
Number of Illustrations
122 b/w illustrations
Topics