โ Scribed by Randall J. LeVeque (auth.)
No coin nor oath required. For personal study only.
Front Matter....Pages i-viii
Front Matter....Pages ix-ix
Introduction....Pages 1-13
The Derivation of Conservation Laws....Pages 14-18
Scalar Conservation Laws....Pages 19-40
Some Scalar Examples....Pages 41-50
Some Nonlinear Systems....Pages 51-57
Linear Hyperbolic Systems....Pages 58-69
Shocks and the Hugoniot Locus....Pages 70-80
Rarefaction Waves and Integral Curves....Pages 81-88
The Riemann problem for the Euler equations....Pages 89-93
Front Matter....Pages 95-95
Numerical Methods for Linear Equations....Pages 97-113
Computing Discontinuous Solutions....Pages 114-121
Conservative Methods for Nonlinear Problems....Pages 122-135
Godunovโs Method....Pages 136-145
Approximate Riemann Solvers....Pages 146-157
Nonlinear Stability....Pages 158-172
High Resolution Methods....Pages 173-192
Semi-discrete Methods....Pages 193-199
Multidimensional Problems....Pages 200-207
Back Matter....Pages 208-214
Science, general
๐ SIMILAR VOLUMES
This is a very good book, and covers all the main issues. It is clear and rigorous. Some topics are covered in brief and additional references may be needed to fully understand the topic.
These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave
<p>These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in deยญ veloping, analyzing
<p>This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first