Math 693B - Advanced Numerical Analysis
                           Spring 1995
                         Dr. Kris Stewart
                      (stewart@cs.sdsu.edu)

Text: Scientific Computing, An Introduction with Parallel Computing
      by Gene Golub and James M. Ortega, Academic Press, 1993

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 ucssun1.  Students will be encouraged
to port their codes to the Cray C90 and/or Intel Paragon
supercomputers, as appropriate, to gain an appreciation for
modern high performance computing tradeoffs.

        We will need in the Xterm Lab BA113 for the first four
Wednesdays of the semester (Feb. 1, 8, 15, 22)

        Feb. 1 will present an introduction to the Symbolic
Computing Environment of Maple.

        The course will cover the following chapter in the text,
which was also used for the first semester of the course:

Chapter 3. Parallel and Vector Computing

Chapter 5. Continuous Problem Solved Discretely

                Augmented by class handouts on

                        Ordinary Differential Equations
                        Boundary Value Problems in ODES
                        Shooting Methods

                        Parabolic Partial Differential Equations

Chapter 7. Parallel Direct Methods (for solving linear systems)

Chapter 8. Iterative Methods (for elliptic PDEs)

Chapter 9. Conjugate Gradient-Type Methods (for elliptic PDEs)

Class handouts on Hyperbolic PDES (covered only superficially)