Finite Difference Methods for Ordinary and Partial Differential Equations,
Randall J LeVeque. SIAM. ISBN 978-0-898716-29-0
Numerical Methods for Conservation Laws, Randall J LeVeque. Springer 1992. ISBN 978-3-0348-8629-1
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic
Conservation Laws, Chi-Wang Shu, NASA/CR-97-206253. ICASE Report No. 97-65
Spectral Methods for Time-dependent problems,
Jan S. Hesthaven, Sigal Gottlieb, David Gottlieb,
Cambridge Monographs on Applied and Computational Mathematics, Series Number 21
K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential Equations, 2nd
The first topic to cover is the finite difference methods for both boundary value problems and
initial value problems. The focus is on building an understanding of
the development, analysis and practical use of finite difference methods for parabolic, elliptic equations
and hyperbolic conservation laws. The concept of consistency, stability, and convergence will be reviewed.
The second topic is the spectral methods. Basic theoretical framework will be covered. It will be applied to solve
1D and 2D non-linear Schrodinger equation.
Regular homework and programming projects will be assigned every one or two
weeks. Allowed programming languages include: Matlab, Fortran, C, C++, Python, Julia.
Grades will be based on homework and programming projects.