Time-Dependant Partial Differential Equations and Their Numerical Solution (Lectures in Mathematics. ETH Zürich)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: May 11, 2001
Language: eng
Format: Paperback
Number of pages: 92
ISBN-13: 9783764361259
Subjects: Differential Equations; Numerical analysis; Science/Mathematics; Numerical Solutions Of Differential Equations; Mathematics; Applied; Differential Equations - Partial Differential Equations; Mathematics / General; PDE
Description: 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.