Time-Dependent Partial Differential Equations and Their Numerical Solution

Name: Time-Dependent Partial Differential Equations and Their Numerical Solution
Price: 39.26 USD
Availability: InStock
ISBN: 9783764361259

ISBN-10: 3764361255

ISBN-13: 9783764361259

Edition: 2001

Authors: Heinz-Otto Kreiss, Hedwig Ulmer Busenhart

List price: $79.99

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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…

Book details

List price: $79.99
Copyright year: 2001
Publisher: Springer Basel AG
Publication date: 4/1/2001
Binding: Paperback
Pages: 82
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 0.352
Language: English



Preface



Cauchy Problems


Well-Posedness


Hyperbolic Systems with Constant Coefficients


General Systems with Constant Coefficients


Linear Systems with Variable Coefficients



Half Plane Problems


Hyperbolic Systems in One Dimension


Hyperbolic Systems in Two Dimensions


Well-Posed Half Plane Problems


Well-Posed Problems in the Generalized Sense


Farfield Boundary Conditions


Energy Estimates


First Order Systems with Variable Coefficients



Difference Methods


Periodic Problems


Half Plane Problems


Method of Lines



Nonlinear Problems


Initial Value Problems for Ordinary Differential Equations


Existence Theorems for Nonlinear Partial Differential Equations


Perturbation Expansion


Convergence of Difference Methods


Bibliography


Index