Math 609-601 Numerical Methods I, Fall 2006

Math 609

Section 601, Fall 2006

Instructor: Dr. Raytcho Lazarov
TA: Dimitar Trenev
- E-mail - trenev@math.tamu.edu
- Office - Blocker 505E
- Office Hours - by appointment
  (although feel free to come to my office any time)
- Phone - 845-7652
Place and Time: (Note the room change!)

Day Time Room

Tuesday 9:35-10:25pm BLOC 125
Helpful Links:
- Dr. Lazarov's Math 609 Page available here.
- Getting Started with LaTeX, Tips for Figures and Tables in LaTeX

Math609 Lab FAQ (each week more Q&A will be added here)
- How to write your reports?
  - You will need to turn in a report for each programming assignment.
    Your report should be a PDF file looking like this : report.pdf.
    Here is the LaTeX source used to create this PDF file : report.tex, graph.eps
  - To produce a .DVI file from your .TEX file, use the command: latex [name_of_file].tex You can view the .DVI file using the program 'xdvi'.
  - To convert your .DVI file to a .PS/.PDF file use the commands 'dvips' or 'dvipdf'.
Past Labs:
- Lab 1 (08/29) : General discussion. A simple solver for triangular matrices.
- Lab 2 (09/05) : A Gaussian elimination solver (with partial row pivoting).
- Lab 3 (09/12) : Review for Programming Assignment #1
  - An example of how to write some data in a file
  - An example of how to use data from a file to create plots with Matlab.
  - A C++ example of how to call the DGESV routine from the LAPACK library.
- Lab 4 (09/19) : A Property of the SSOR Iteration Matrix. Discussion of Programming Assignment #1.
  - Here's a PDF file explaining the derivation of the SSOR splitting matrix. I wrote it this morning so there may still be some typos in it. In any case, we'll go over it in class next time (if you have any questions).
- Lab 5 (09/26) : The Conjugate Gradient Algorithm.
  - Discussion of the Error Reduction (and How it Depends on the Condition Number of A).
  - Here's an implementation of the CG algorithm, solving the system from Problem 2 of your first Programming Assignment.
- Labs 6 and 7 (10/03 and 10/10) : Programming Assignment #2.
  - Discussion of the the third programming assignment.
  - Here's an implementation of the Chebyshev acceleration applied to the Richardson Iteration, solving the system from page 243 of your text books.
- Lab 8 (10/17) : Programming Assignment #3.
  - Discussion of the the third programming assignment.
  - Here's an example of how your data file should look like (this is the actual data file for Problem 2 in your programming assignment), and how you can access that data from a c++ program.
- Lab 9 (10/24) : Richardson Extrapolation
  - Discussion of the Richardson extrapolation technique.
  - Here's an implementation of this technique for a simple numerical differentiation formula.
- Lab 10 (10/31) : Runge-Kutta methods
  - Discussion of some homework problems.
  - And an implementation of the second order Runge-Kutta method from your textbooks.
- Lab 11 (11/07) : A discussion (Problem #5 from Homework Assignment #6)
  - Full solution of problem #5 from HW #6.
  - An empirical "proof" that the value of h we found indeed performs best.
- Lab 12 (11/14) : Stiff equations, A-Stability.
  - An example on the black board.
  - A program illustrating the performance of the (A-stable) Implicit Euler method and the Explicit Euler method on a stiff equation.
- Lab 13 (11/21) : Programming Assignment #4.
  - Discussion of the the fourth programming assignment.
  - An example of a method (RKF45) that automatically adjusts the step size to keep the local truncation error below a certain prescribed tolerance.

Day	Time	Room
Tuesday	9:35-10:25pm	BLOC 125