Mathematical Modeling of Melting and Freezing Processes Hemisphere Publ. Co., 1993

Numerical Modeling in Science and Engineering, Wiley, 1988

Introduction to High Performance Scientific Computing , Lulu.com, 2010, $18 , free download.

Numerical Computing with Modern Fortran, SIAM, 2013 (

Introduction to the Foundations of Applied Mathematics , Springer, 2009

Numerical Methods for Conservation Laws, Birkhauser, 1990

Finite Volume Methods for Hyperbolic Problems, Cambridge U Press, 2002, ISBN 0-521-00924-3

Introduction to Parallel Computing, Oxford U Press, 2004 (paperback)

Numerical Recipes in Fortran (or C) , Cambridge U Press, 1992

Introduction to Partial Differential Equations - A Computational Approach, Springer, 2005

Numerical Methods for Differential Equations, Prentice Hall, 1992

Numerical Solution of PDEs, Cambridge U Press, 1994

Numerical Computation in Science and Engineering, Oxford U Press, 1998 (I haven't seen it)

Conservative Finite-Difference Methods On General Grids, CRC Press, 1996

Numerical Partial Differential Equations: Finite Difference Methods, Springer-Verlag, 1995

Advanced Scientific Fortran, Wiley, 1995

**Some interesting relevant papers**

PDEs for self-organization in cellular and developmental biology , Nonlinearity 21(11): R251, 2008

(nice survey paper of PDEs in action. Derivation as in class and many others...)

On the Modeling of Traffic and Crowds, SIAM Review 53(3): 409-463

(nice FV paper, with good test problems)

A high order sharp-interface method with local time stepping for compressible multiphase flows.,

Commun. Comput. Phys., 9: 205-230, 2011

(for shock tracking via combination of high resolution methods, uses FV, WENO, DG, local time-stepping, ...)

Advanced numerical approximation of nonlinear hyperbolic equations

Springer Lecture Notes Math. no.1697, 1998 QA3.L28 no.1697

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems ,

SIAM Review 51 (1):82-126, 2009 (excellent review by the master)

Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: Survey and new developments

Proc. R. Soc. A, may 2011 (excellent)

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes

Journal of Scientific Computing, 50(1): 29-62, 2012 (excellent, also for FV schemes)

Computational Approaches to Solving Equations Arising from Wound Healing ,

Bulletin of Mathematical Biology, 71(1):211-246, 2009 (good overview/comparison of FV methods)

Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes ,

Commun. Comput. Phys., 1: 192-206, 2006