Homework for MATH712, Fall 2001

Homework/Project assignments for Spring 2002

The homework assignments will sometimes be distributed as PDF or PS files. Hold the SHIFT key and left click on the link to download, or just click on the link to view online. Extensive on-line help on Matlab is available within the program itself, and also here (note: some links pertain to ODE's).

Homework 1 (DUE Tuesday, Jan. 29): Do problem 4.2.1 from Thomas' book. Determine the stability condition through numerical experimentation using your program. Produce surface plots of the solution at t=0.9 obtained with the two timesteps given in the problem statement.
Homework 2 (DUE Tuesday, Feb. 12): Write a program to implement an explicit finite difference scheme (first-order accurate in time, and second-order accurate in space) to solve the nonlinear IBVP for the reaction-diffusion system of PDE's studied in this paper. Use your code to reproduce Figure 13d) of the paper. NOTE: I did some timed test runs of the HW2 program with a domain size of 201X201 grid points using h=0.2. I found that the mathsun computers (for 201X201 points) can execute about 1750 timesteps per minute if yours is the only job running. If two jobs are running then it will be 1750 timesteps per _two_ minutes, and so on and so forth. Thus, to estimate in minutes the smallest time your run will take to complete divide your NTOTAL (total number of timesteps) with 1750. Do not forget to account for other jobs running on the machine you chose to run your job on.
Homework 3 (DUE Thursday, March 7): Here is the HW description. This FORTRAN program will be useful. Also, you may find the MATH712 HW2 programs useful.
Homework 4 NOTE: You should make x be in the interval [-pi,pi], and Equation (4) should read u(x,t)=c-2... (DUE Thursday, March 28)
Homework 5 (DUE Thursday, April 11): Here are two programs, testcf.f and testcm.f, that implement Chebyshev pseudospectral differentiation using the FFT and matrix approaches respectively. Read them, and try them out to see how they work. Here is the Homework 5 statement.

Final Project for Spring 2002
Here is the description of the final project. Here is a useful code for the final project.