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© 2001

Time-dependent Partial Differential Equations and Their Numerical Solution

Book

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

Table of contents

  1. Front Matter
    Pages i-vii
  2. Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 1-20
  3. Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 21-46
  4. Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 47-65
  5. Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
    Pages 67-77
  6. Back Matter
    Pages 79-82

About this book

Introduction

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.

Keywords

Cauchy problem PDE boundary element method convergence differential equation hyperbolic system nonlinear partial differential equation ordinary differential equation partial differential equation stability

Authors and affiliations

  1. 1.Department of MathematicsUniversity of California Los AngelesLos AngelesUSA
  2. 2.ZürichSwitzerland

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
  • Copyright Information Birkhäuser Verlag, P.O. Box 133,CH-4010 Basel,Switzerland 2001
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-7643-6125-9
  • eBook ISBN 978-3-0348-8229-3
  • Edition Number 1
  • Number of Pages VIII, 82
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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