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By Randall J. LeVeque
Publisher: Cambridge University Press
Print Publication Year:2002
Online Publication Date:September 2012
Online ISBN:9780511791253
Hardback ISBN:9780521810876
Paperback ISBN:9780521009249
Book DOI: http://dx.doi.org/10.1017/CBO9780511791253
Subjects: Numerical Analysis and Computational Science , Geometry and Topology
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 applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. 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.
Reviews:
pp. i-viii
pp. ix-xvi
pp. xvii-xx
pp. 1-12
Part I - Linear Equations: Read PDF
pp. 13-14
2 - Conservation Laws and Differential Equations: Read PDF
pp. 15-46
3 - Characteristics and Riemann Problems for Linear Hyperbolic Equations: Read PDF
pp. 47-63
4 - Finite Volume Methods: Read PDF
pp. 64-86
5 - Introduction to the CLAWPACK Software: Read PDF
pp. 87-99
6 - High-Resolution Methods: Read PDF
pp. 100-128
7 - Boundary Conditions and Ghost Cells: Read PDF
pp. 129-138
8 - Convergence, Accuracy, and Stability: Read PDF
pp. 139-157
9 - Variable-Coefficient Linear Equations: Read PDF
pp. 158-187
10 - Other Approaches to High Resolution: Read PDF
pp. 188-200
Part II - Nonlinear Equations: Read PDF
pp. 201-202
11 - Nonlinear Scalar Conservation Laws: Read PDF
pp. 203-226
12 - Finite Volume Methods for Nonlinear Scalar Conservation Laws: Read PDF
pp. 227-252
13 - Nonlinear Systems of Conservation Laws: Read PDF
pp. 253-290
14 - Gas Dynamics and the Euler Equations: Read PDF
pp. 291-310
15 - Finite Volume Methods for Nonlinear Systems: Read PDF
pp. 311-349
16 - Some Nonclassical Hyperbolic Problems: Read PDF
pp. 350-374
17 - Source Terms and Balance Laws: Read PDF
pp. 375-418
Part III - Multidimensional Problems: Read PDF
pp. 419-420
18 - Multidimensional Hyperbolic Problems: Read PDF
pp. 421-435
19 - Multidimensional Numerical Methods: Read PDF
pp. 436-446
20 - Multidimensional Scalar Equations: Read PDF
pp. 447-468
21 - Multidimensional Systems: Read PDF
pp. 469-490
pp. 491-513
23 - Finite Volume Methods on Quadrilateral Grids: Read PDF
pp. 514-534
pp. 535-552
pp. 553-558