Time-dependent Partial Differential Equations and Their Numerical Solution

✍ Scribed by Heinz-Otto Kreiss, Hedwig Ulmer Busenhart (auth.)

• Publisher: Birkhäuser Basel
• Year: 2001
• Tongue: English
• Leaves: 86
• Series: Lectures in Mathematics. ETH Zürich
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vii
Cauchy Problems....Pages 1-20
Half Plane Problems....Pages 21-46
Difference Methods....Pages 47-65
Nonlinear Problems....Pages 67-77
Back Matter....Pages 79-82

✦ Subjects

Mathematics, general