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

edition, Cambridge

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.

## Department of Mathematics and Statistics