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  • © 2014

Analysis of Finite Difference Schemes

For Linear Partial Differential Equations with Generalized Solutions

  • 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

  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 46)

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Price excludes VAT (USA)
  • ISBN: 978-1-4471-5460-0
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Softcover Book USD 129.00
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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XIII
  2. Distributions and Function Spaces

    • Boško S. Jovanović, Endre Süli
    Pages 1-90
  3. Elliptic Boundary-Value Problems

    • Boško S. Jovanović, Endre Süli
    Pages 91-243
  4. Finite Difference Approximation of Parabolic Problems

    • Boško S. Jovanović, Endre Süli
    Pages 245-325
  5. Finite Difference Approximation of Hyperbolic Problems

    • Boško S. Jovanović, Endre Süli
    Pages 327-387
  6. Back Matter

    Pages 389-408

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.

Keywords

  • Bramble-Hilbert Lemma
  • Energy Estimates
  • Error Analysis
  • Finite Difference Methods
  • Generalized Solutions
  • Mollifiers
  • Numerical Analysis of Partial Differential Equations
  • Stability
  • 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)

Authors and Affiliations

  • Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Boško S. Jovanović

  • Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Endre Süli

Bibliographic Information

  • Book Title: Analysis of Finite Difference Schemes

  • Book Subtitle: For Linear Partial Differential Equations with Generalized Solutions

  • Authors: Boško S. Jovanović, Endre Süli

  • Series Title: Springer Series in Computational Mathematics

  • DOI: https://doi.org/10.1007/978-1-4471-5460-0

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London 2014

  • Hardcover ISBN: 978-1-4471-5459-4

  • Softcover ISBN: 978-1-4471-7259-8

  • eBook ISBN: 978-1-4471-5460-0

  • Series ISSN: 0179-3632

  • Series E-ISSN: 2198-3712

  • Edition Number: 1

  • Number of Pages: XIII, 408

  • Number of Illustrations: 7 illustrations in colour

  • Topics: Numerical Analysis, Differential Equations

Buying options

eBook USD 99.00
Price excludes VAT (USA)
  • ISBN: 978-1-4471-5460-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 129.00
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)