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Time-Dependent Partial Differential Equations and Their Numerical Solution

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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…    
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Book details

List price: $79.99
Copyright year: 2001
Publisher: Birkh�user Boston
Publication date: 4/1/2001
Binding: Paperback
Pages: 82
Size: 6.75" wide x 9.25" long x 0.50" tall
Weight: 0.440
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