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Finite Difference Methods for Ordinary and Partial Differential
Equations, Steady State and Time Dependent Problems
by Randall J. LeVeque, SIAM, 2007
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Finite Volume Methods for Hyperbolic Problems, by Randall J. LeVeque, Cambridge University Press, 2002.
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Numerical Methods for Conservation Laws, by Randall J. LeVeque, Lectures in Mathematics, ETH-Zurich Birkhauser-Verlag, Basel, 1990. ISBN 3-7643-2464-3
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Computational Methods for Astrophysical Fluid Flow, by R. J. LeVeque, D. Mihalas, E. Dorfi,and E. Mueller, 27th Saas-Fee Advanced Course Lecture Notes, Edited by O. Steiner and A. Gautschy, Springer-Verlag, 1998.
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Discrete Mathematical Modeling .
Class Notes from Math 381, Autumn 1999 are available in postscript
These notes have been further revised, primarily by Tim Chartier and Anne Greenbaum. A more recent version is available from the Winter 2003 class webpage
Please contact me if you wish to use these notes in a course elsewhere.
Eventually they may be expanded into a book.