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 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/

List of Topics:

• 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.

Resources:

• MCS 571 Handouts and Demonstrations.

• Text for "Second Opinion (Course is Lecture Based)":
  1. 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":

  1. 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).

  2. A. R. Mitchell and D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, April 2001, out of print).

  3. F. B. Hanson, Markov Chain Approximation, Section from Chapter listed next
     
     Click for FTP Postscript Copy (100K)?

  4. 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. ,
     
     Click for FTP widepage Postscript Copy (400K)?

  5. J. R. Shewchuck, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain,
     • Click for FTP Text Abstract Copy?
     • Click for FTP Postscript Copy (2MB, 58 pages)?

  6. G. Golub and J. M. Ortega, Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993. (see CGM description)

  7. James M. Ortega, Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, 1988. (see CGM description)

  8. D. Tavella and C. Randall, Pricing Financial Instruments: The Finite Difference Method, Wiley, 2000.

  9. P. Wilmott, Derivatives: The Theory and Practice of Financial Engineering, John Wiley, New York, 1998.

  10. Desmond J. Higham and Nicolas J. Higham, MATLAB Guide, SIAM, 2000.

  11. Duane Hanselman and Bruce Littlefield, Mastering MATLAB 6: A Comprehensive Tutorial and Reference, Prentice Hall, 2001.

  12. Delores M. Etter, Engineering Problem Solving with MATLAB, Prentice Hall,1993.

  13. George Lindfield and John Penny, Numerical Methods Using MATLAB, Prentice Hall, 2000.

  14. 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%

Take-Home Exams (3: PPDE, EPDE & HPDE):

PDE Take-Home Exams will be Announced When Topic has been Discussed in Lectures and When Problem is Ready:

• PPDE Exam Spring 2004 (PDF Copy), Due Wednesday, 17 March 2004 in Class

• EPDE Exam Spring 2004 (PDF Copy), Due Wednesday, 21 April 2004 in Class

• HPDE Exam Spring 2004 (PDF Copy), Due Wednesday, 05 May 2004 in 718 SEO

• Computer Project 1: Numerical PPDE Methods, Due Monday 05 April 2005 in Class

• Computer Project 2: Numerical EPDE Methods, Due Wednesday 28 April 2005 in Class

Practice Problems:

• Click for PPDE Practice Problems in HTML Format Copy?

• Old PPDE Exam Postscript Copy?

• EPDE Practice Problems:  
  1. Click to FTP Postscript Copy?
  2. Else, Click for rough HTML Copy?

• PPDE/EPDE FEM Simple Example (pseudocode).

• HPDE Practice Problems Problems:  
  1. Click to FTP Postscript Copy?

• OLD Final (EPDE-HPDE) Exam:  
  1. Click to FTP Postscript Copy?