Math 693B - Advanced Numerical Analysis
Spring 1997
BA 254 MW 5-6:15
Dr. Kris Stewart
(stewart@rohan.sdsu.edu)
Text: Scientific Computing, An Introduction with Parallel Computing
by Gene Golub and James M. Ortega, Academic Press, 1993
OH: MW 2-3:15
Prerequisite: Math 693a
The second semester of this course pursues investigations
into method to solve differential equations. Differential
equations describe most of the processes in science involving
change. The numerical techniques to effectively solve such
problems are well established for the class of ordinary
differential equations (i.e. searching for a solution that is a
function of a single independent variable). For the class of
partial differential equations, the solution techniques are
typically tailored to the "class" of problem, either parabolic,
elliptic or hyperbolic.
This class involves significant programming assignments to
explore the various solution techniques. In general, high
quality software from well established libraries are used to
perform the bulk of the computation, with the student being
required to write only the main program which directs the flow of
the solution process.
The course will explore the impact of parallel and vector
supercomputers, though most programming will take place on the
SDSU instructional machine rohan. Students will be encouraged to
port their codes to the Cray C90 vector and/or Cray T3E parallel
supercomputers, as appropriate, to gain an appreciation for
modern high performance computing tradeoffs.
We will meet in the Xterm Lab BA113 for four
Wednesdays this semester (Feb. 5, 12, 19, 26)
The course will cover the following chapters in the text,
Ch. 1. The World of Scientific Computing (1/27/97)
Ch. 2. Linear Algebra (you should review on your own)
Ch. 3. Parallel and Vector Computing (1/29/97 & 2/3/97 briefly)
Feb. 5 Lab will present an introduction to the Symbolic Computing
Environment of Maple
Ch. 5. Continuous Problem Solved Discretely (2/10/97 begin)
Augmented by class handouts on
Ordinary Differential Equations
"User's View of Stiffness" Shampine/Gear SIAM Review
Shooting Methods
Feb. 12 Lab - Introduction to writing HTML and your own web page so
that you can begin to develop your own professional portfolio
(which might be useful for job applications later on)
Feb. 19 Lab - Computational Examples for ODEs
Feb. 26 Lab - Info Overload (updated from Fall '96)
Text: 5.4 (3/17/97) Parabolic Partial Differential Equations
Text: 5.3 (3/31/97) Boundary Value Problems in ODES
Text: 5.5 (4/7/97) Elliptic PDEs
Ch. 7. Parallel Direct Methods (for solving linear systems) (4/21/97)
Ch. 8. Iterative Methods (for elliptic PDEs) (4/28/97)
Ch. 9. Conjugate Gradient-Type Methods (for elliptic PDEs)
Text: 5.4 (p. 199) Wave Equation (5/4/97)
Class handouts on Hyperbolic PDES (covered only superficially)
Computational Experiments:
Feb. 26 - Stiffness experiment using explicit Runge-Kutta-Fehlberg solver
Mar. 19 - Stiff/Nonstiff experiment using Adams and BDF predictor/correctors
Apr. 9 - Method of Lines experiment
May 23 - Computational Experiment of your choice (might be beginning
of a thesis investigation)