The assignments include both theoretical problems
and computational projects. Here are some guideline for
doing the computation project:
(1) The program should be written in a relatively formal fashion, be easy to read,
and contain comments of major steps;
(2) Please turn in a disk or email me all your programs and data files that are
necessary to run your programs, including a simple README file.
(3) You are encouraged to discuss with other fellow students, but you need to
finish and turn in your own project
separately.
HW# 1
( on linear transport equations $u_t
=a u_x $.)
HW# 2 ( on 2nd or higher order time-dependent
equations) Due Oct. 14,
Thursday
HW# 3
( on scalar nonlinear conservation laws $u_t +
f(u)_x=0$ ) Due 10, 28,
Thursday
Further computational projects will be on systems of conservation laws.
Project
#1 ( LxF and Roe's
method for 1-D shallow water simulation).
A power-point lecture (Oct. 19) note on nonlinear stability issue can be found here.
Final Project: (LxF and high-resolution
scheme for 1-D full Euler equation simulation)
Examples to be tested can be found
here. This must be turned in by Dec. 10, 5:00pm.