Springer Series in Computational Mathematics

Analysis of Finite Difference Schemes

For Linear Partial Differential Equations with Generalized Solutions

Authors: Jovanović, Boško S., Süli, Endre

  • Develops a systematic and rigorous theory for the construction and analysis of finite difference methods
  • Presents the theory with minimal regularity conditions i.e. for PDEs with nonsmooth solutions and data
  • Partially accessible to advanced undergraduate and masters students interested in numerical analysis
see more benefits

Buy this book

eBook £67.99
price for United Kingdom (gross)
  • ISBN 978-1-4471-5460-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £85.50
price for United Kingdom (gross)
  • ISBN 978-1-4471-5459-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £85.50
price for United Kingdom (gross)
  • ISBN 978-1-4471-7259-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.

Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity.

In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions.

Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Reviews

“While there are plenty of books on finite difference (FD) schemes for linear PDE in case of smooth coefficients and inhomogeneous terms, the literature seems lacking when it comes to the nonsmooth case. This monograph fills the gap. … The text addresses graduate students in mathematics and researchers.” (M. Muthsam, Monatshefte für Mathematik, 2016)

“The authors present a new monograph on finite difference schemes for pde’s with weak solutions. … readable for specialist working in the field of numerical analysis, maybe including excellent graduate students of mathematics. … for scientists interested in the analysis of discretization methods for very weak solutions, including solutions in Besov or Bessel-potential spaces, the monography presents many fruitful ideas and useful ingredients.” (H.-G. Roos, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 94 (11), 2014)


Table of contents (4 chapters)

  • Distributions and Function Spaces

    Jovanović, Boško S. (et al.)

    Pages 1-90

  • Elliptic Boundary-Value Problems

    Jovanović, Boško S. (et al.)

    Pages 91-243

  • Finite Difference Approximation of Parabolic Problems

    Jovanović, Boško S. (et al.)

    Pages 245-325

  • Finite Difference Approximation of Hyperbolic Problems

    Jovanović, Boško S. (et al.)

    Pages 327-387

Buy this book

eBook £67.99
price for United Kingdom (gross)
  • ISBN 978-1-4471-5460-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £85.50
price for United Kingdom (gross)
  • ISBN 978-1-4471-5459-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £85.50
price for United Kingdom (gross)
  • ISBN 978-1-4471-7259-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Analysis of Finite Difference Schemes
Book Subtitle
For Linear Partial Differential Equations with Generalized Solutions
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
46
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4471-5460-0
DOI
10.1007/978-1-4471-5460-0
Hardcover ISBN
978-1-4471-5459-4
Softcover ISBN
978-1-4471-7259-8
Series ISSN
0179-3632
Edition Number
1
Number of Pages
XIII, 408
Number of Illustrations and Tables
7 illustrations in colour
Topics