Product Description

This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Product Details

• Amazon Sales Rank: #416796 in Books
• Published on: 2002-08-26
• Original language: English
• Number of items: 1
• Binding: Paperback
• 578 pages

Review
'It is moreover advantageous that the algorithms presented are public and easily available via the web-page cited. Similar to the book of R. J. LeVeque titled Numerical Methods for Conservation Laws, this manuscript will certainly become a part of the standard literature in the field of numerical methods for hyperbolic partial differential equations.' Journal of Applied Mathematics and Physics

‘The text is very well written and can serve for self-study as well as an accompanying text book for teaching purposes … a very sound and comprehensive introduction into hyperbolic problems and their numerical treatment.’ Zentralblatt MATH

Customer Reviews

Readable "hands-on" text from a recognised expert in the field
Clear exposition of numerical methods for hyperboilic equations. No lengthy proofs, but enough material to get you write your own codes within a couple of weeks. A lot of physics, which is something you would hardly expect from a book like this. The author sometimes takes an intuitive approach rather than bombarding you with long derivations. So if you are just starting your work on Riemann solvers, this is the Book for you. Worth every penny.