Numerical Methods for Conservation Laws

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.

"The computing community needs a good text on modern methods for conservation laws, and these notes provide an excellent start on that text. Equally important, LeVeque's perspective and writing style make for wonderful reading and learning. (How often do we find important content and good writing in one book?)"   —SIAM Review
"The book by Randall LeVeque is among the first that makes the material in this area accessible to first and second year graduate students in the mathematical sciences. It should be an excellent introduction to this topic for any researcher in the mathematical sciences…This book is based on [the] lecture notes of the author and should serve well as a text for a graduate course…There are many interesting exercises that serve to illuminate and expand on the text, and there are also many well-drawn figures."   —Bulletin of the AMS