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  • Textbook
  • © 2014

Numerical Models for Differential Problems

  • Author faces here the basic concepts for the numerical modeling of partial differential equations

  • An outstanding reference work in this branch of applied mathematics

  • In particular, the author discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs

  • Includes supplementary material: sn.pub/extras

Part of the book series: MS&A (MS&A, volume 8)

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eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-88-470-5522-3
  • Instant PDF download
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Softcover Book USD 74.99
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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XIX
  2. Elements of functional analysis

    • Alfio Quarteroni
    Pages 11-29
  3. Elliptic equations

    • Alfio Quarteroni
    Pages 31-60
  4. Parabolic equations

    • Alfio Quarteroni
    Pages 121-140
  5. Generation of 1D and 2D grids

    • Alfio Quarteroni
    Pages 141-159
  6. Algorithms for the solution of linear systems

    • Alfio Quarteroni
    Pages 161-177
  7. Elements of finite element programming

    • Alfio Quarteroni
    Pages 179-212
  8. The finite volume method

    • Alfio Quarteroni
    Pages 213-223
  9. Spectral methods

    • Alfio Quarteroni
    Pages 225-266
  10. Discontinuous element methods (DG and mortar)

    • Alfio Quarteroni
    Pages 267-289
  11. Diffusion-transport-reaction equations

    • Alfio Quarteroni
    Pages 291-338
  12. Finite differences for hyperbolic equations

    • Alfio Quarteroni
    Pages 339-370
  13. Nonlinear hyperbolic problems

    • Alfio Quarteroni
    Pages 409-428
  14. Navier-Stokes equations

    • Alfio Quarteroni
    Pages 429-482
  15. Optimal control of partial differential equations

    • Alfio Quarteroni
    Pages 483-525
  16. Domain decomposition methods

    • Alfio Quarteroni
    Pages 527-584

About this book

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Keywords

  • PDE
  • analysis
  • numerical modelling

Authors and Affiliations

  • CMCS-MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Switzerland

    Alfio Quarteroni

  • MOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Italy

    Alfio Quarteroni

About the author

The Author is Professor and Director of the Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998, Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989, and Scientific Director of MOX, since 2002. Author of 22 books published with Springer, and of about 200 papers published in refereed international Journals, Conference Proceedings and Magazines, Alfio Quarteroni is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC.

Bibliographic Information

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-88-470-5522-3
  • 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 74.99
Price excludes VAT (USA)