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Numerical methods for conservation laws / Randall J. LeVeque.

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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...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Author: LeVeque, Randall J., 1955-
Format: eBook
Language:English
Published: Basel ; Boston : Birkhäuser Verlag, 1992.
Edition:2nd ed.
Series:Lectures in mathematics ETH Zürich.
Subjects:
Differential equations, Hyperbolic > Numerical solutions.
Conservation laws (Mathematics)
Shock waves.
Table of Contents:
  • I Mathematical Theory
  • 1 Introduction
  • 2 The Derivation of Conservation Laws
  • 3 Scalar Conservation Laws
  • 4 Some Scalar Examples
  • 5 Some Nonlinear Systems
  • 6 Linear Hyperbolic Systems 58
  • 7 Shocks and the Hugoniot Locus
  • 8 Rarefaction Waves and Integral Curves
  • 9 The Riemann problem for the Euler equations
  • II Numerical Methods
  • 10 Numerical Methods for Linear Equations
  • 11 Computing Discontinuous Solutions
  • 12 Conservative Methods for Nonlinear Problems
  • 13 Godunov's Method
  • 14 Approximate Riemann Solvers
  • 15 Nonlinear Stability
  • 16 High Resolution Methods
  • 17 Semi-discrete Methods
  • 18 Multidimensional Problems.

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