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Time-dependent Partial Differential Equations and Their Numerical Solution

  • Heinz-Otto Kreiss
  • Hedwig Ulmer Busenhart

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

  • Heinz-Otto Kreiss
    • 1
  • Hedwig Ulmer Busenhart
    • 2
  1. 1.Department of MathematicsUniversity of California Los AngelesLos AngelesUSA
  2. 2.ZürichSwitzerland

Bibliographic information

  • 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
  • Print ISBN 978-3-7643-6125-9
  • Online ISBN 978-3-0348-8229-3
  • Buy this book on publisher's site