MCS 571 Numerical Methods for Partial Differential Equations
--- Spring 2004
Syllabus and Class HomePage
|
MATLABHelp
|
MapleHelp
|
Resources
|
Department: Math, Statistics, and Computer Science
Time Table Spring 2004:
06967 LECD 0200-0250 M W F 0216 TH
Lecturer: F. B. Hanson, 718 SEO, X3-2142 (X6-3041msg)
Course Coordinator: F. B. Hanson, 718 SEO, X3-2142 (X6-3041msg)
- Office Hours: 1PM-1:50PM MWF 718 SEO,
but will answer any questions in classroom at end of each MCS571 class.
- E-Mail:
hanson A T uic edu
- Instructor Web Page: http://www.math.uic.edu/~hanson/
- Class Web Page (this page): http://www.math.uic.edu/~hanson/mcs571/
Catalog description:
Finite difference methods for parabolic, elliptic and hyperbolic
differential equations: explicit, Crank-Nicolson implicit,
alternating directions implicit, upwinding, Jacobi, Gauss-Seidel,
successive over-relaxation, conjugate gradient,
Lax-Wendroff, Fourier stability.
Prerequisites:
Graduate standing and Math 481 Applied Partial Differential Equations
and MCS 471 Numerical Analysis OR consent of the instructor
Semester Credit hours: 3U4G
-
Numerical Methods for Parabolic PDEs;
review and generalization of finite difference methods, explicit methods,
Crank-Nicolson implicit method, Fourier stability methods,
alternating directions implicit method, upwinding,
higher level schemes, nonlinear equations, predictor corrector methods,
financial engineering applications, computer problems. 7.5 weeks.
-
Numerical Methods for Elliptic PDEs; analytical methods, Jacobi's
method, Gauss-Seidel method, successive over-relaxation method,
rates of convergence, alternating directions implicit method,
conjugate gradient method, Galerkin finite element method, irregular regions,
artificial boundaries, computer problems. 4 weeks.
-
Numerical methods for hyperbolic PDEs; explicit methods,
D'Alembert's exact solution, method of characteristics,
Lax-Wendroff method, method of artificial viscosity, higher dimensions,
Courant-Friedrichs-Lewy condition, curvilinear characteristics,
computer implementations. 3.5 weeks.
-
Total including leeway. 15 weeks.
-
MCS 571 Handouts and Demonstrations.
- Text for "Second Opinion (Course is Lecture Based)":
- K. W. Morton and D. F. Mayers, Numerical Solution of Partial
Differential Equations, Cambridge University Press, New York, 1993
(ISBN: 052142922, Paperback, Amazon price $27.95).
- Supplementary Texts for "Third or More Opinions":
- Gordon D. Smith,
Numerical Solution of Partial Differential Equations : Finite Difference
Methods, 3rd Edition, Oxford Univ Press, 1986 (ISBN: 0198596502,
Paperback, Amazon Price $45.95).
- A. R. Mitchell and D. F. Griffiths,
The Finite Difference Methods in Partial Differential Equations,
Wiley, April 2001, out of print).
-
F. B. Hanson, Markov Chain Approximation, Section from Chapter
listed next
-
F. B. Hanson,
"Techniques in Computational Stochastic Dynamic Programming"
in Stochastic Digital Control System Techniques,
within series Control and Dynamic Systems: Advances in Theory and
Applications, vol. 76, (C. T. Leondes, Editor), Academic Press,
New York, NY, pp. 103-162, April 1996.
,
-
J. R. Shewchuck, An Introduction to the Conjugate Gradient Method
Without the Agonizing Pain,
-
G. Golub and J. M. Ortega, Scientific Computing: An Introduction with
Parallel Computing, Academic Press, 1993. (see CGM description)
-
James M. Ortega, Introduction to Parallel and Vector Solution
of Linear Systems, Plenum Press, 1988. (see CGM description)
-
D. Tavella and C. Randall, Pricing Financial Instruments: The Finite
Difference Method, Wiley, 2000.
-
P. Wilmott, Derivatives: The Theory and Practice of Financial
Engineering, John Wiley, New York, 1998.
- Desmond J. Higham and Nicolas J. Higham,
MATLAB Guide, SIAM, 2000.
- Duane Hanselman and Bruce Littlefield, Mastering MATLAB 6:
A Comprehensive Tutorial and Reference, Prentice Hall, 2001.
- Delores M. Etter,
Engineering Problem Solving with MATLAB, Prentice Hall,1993.
- George Lindfield and John Penny,
Numerical Methods Using MATLAB, Prentice Hall, 2000.
- Rudra Pratap,
Getting Started with MATLAB, Saunders, 1996.
- Help On-Line for PDE Texts and Tools:
(Click Here for HTML Page)
-
Supplementary References in Numerical Analysis:
(Click Here for HTML Page)
-
Help for Numeric and Symbolic Computational Tools:
(Click Here for HTML Page)
Grading Policy:
- 3 Computer Projects = 50%
- 2 Take Home Exams = 50%
- 3 Practice Problems Sets = 00%
PDE Take-Home Exams will be Announced
When Topic has been Discussed in
Lectures and When Problem is Ready:
PDE Computer Projects will be Announced
When Topic has been Discussed in
Lectures and When Problem is Ready:
Web Source: http://www.math.uic.edu/~hanson/mcs571
Email Comments or Questions to
hanson A T uic edu