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Time-dependent Partial Differential Equations and Their Numerical Solution

  • Book
  • © 2001

Overview

Authors:
  1. Heinz-Otto Kreiss

    1. Department of Mathematics, University of California Los Angeles, Los Angeles, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Hedwig Ulmer Busenhart

    1. Zürich, Switzerland

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lectures in Mathematics. ETH Zürich (LM)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-vii
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  2. Cauchy Problems

    • Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 1-20

  3. Half Plane Problems

    • Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 21-46

  4. Difference Methods

    • Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 47-65

  5. Nonlinear Problems

    • Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 67-77

  6. Back Matter

    Pages 79-82
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Keywords

About this book

In these notes we study time-dependent partial differential equations and their numerical solution. The analytic and the numerical theory are developed in parallel. For example, we discuss well-posed linear and nonlinear problems, linear and nonlinear stability of difference approximations and error estimates. Special emphasis is given to boundary conditions and their discretization. We develop a rather general theory of admissible boundary conditions based on energy estimates or Laplace transform techniques. These results are fundamental for the mathematical and numerical treatment of large classes of applications like Newtonian and non-Newtonian flows, two-phase flows and geophysical problems.

Authors and Affiliations

  • Department of Mathematics, University of California Los Angeles, Los Angeles, USA

    Heinz-Otto Kreiss

  • Zürich, Switzerland

    Hedwig Ulmer Busenhart

Bibliographic Information

  • Book Title: Time-dependent Partial Differential Equations and Their Numerical Solution

  • Authors: Heinz-Otto Kreiss, Hedwig Ulmer Busenhart

  • Series Title: Lectures in Mathematics. ETH Zürich

  • DOI: https://doi.org/10.1007/978-3-0348-8229-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2001

  • Softcover ISBN: 978-3-7643-6125-9Published: 01 April 2001

  • eBook ISBN: 978-3-0348-8229-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 82

  • Topics: Analysis

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