MCS 571 Numerical Methods for Partial Differential Equations
 Spring 2004
Syllabus and Class HomePage

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Department: Math, Statistics, and Computer Science
Time Table Spring 2004:
06967 LECD 02000250 M W F 0216 TH
Lecturer: F. B. Hanson, 718 SEO, X32142 (X63041msg)
Course Coordinator: F. B. Hanson, 718 SEO, X32142 (X63041msg)
 Office Hours: 1PM1:50PM MWF 718 SEO,
but will answer any questions in classroom at end of each MCS571 class.
 EMail:
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, CrankNicolson implicit,
alternating directions implicit, upwinding, Jacobi, GaussSeidel,
successive overrelaxation, conjugate gradient,
LaxWendroff, 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,
CrankNicolson 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, GaussSeidel method, successive overrelaxation 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,
LaxWendroff method, method of artificial viscosity, higher dimensions,
CourantFriedrichsLewy 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. 103162, 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 OnLine 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 TakeHome 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