MCS 571 Numerical Methods for Partial Differential Equations --- Spring 1997

Syllabus And Class HomePage

• Office Hours: 1+PM MWF 718 SEO, but starting after class in 320TH

• E-Mail: Hanson@uic.edu

• Instructor Web Page: http://www.math.uic.edu/~hanson/

• Class Web Page: http://www.math.uic.edu/~hanson/mcs571syllabus.html/

• Numerical Methods for Parabolic PDEs; review of finite difference methods, explicit methods, Crank-Nicolson implicit method, Fourier stability methods, alternating directions implicit method, higher level schemes, nonlinear equations, predictor corrector methods, computer problems. 15 hours.
• 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 method, irregular regions, artificial boundaries, computer problems. 15 hours.
• 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, computer implementations. 12 hours.
• Leeway. 3 hours.
• Total. 45 hours.

• K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, New York, 1994.

• A. R. Mitchell and D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, 1980.
• F. B. Hanson, Markov Chain Approximation, Section from Chapter listed next
  
  Click for FTP Postscript Copy (100K)?
• 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)?
• J. R. Shewchuck, ``An Introduction to the Conjugate Gradient Method Without the Agonizing Pain'',
  1. Click for FTP Text Abstract Copy?
  2. Click for FTP Postscript Copy (2MB, 58 pages)?
• 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)

• 2 Computer Problems = 50%
• 2 Take Home Exams = 50%
• 3 Practice Problems Sets = 00%

• PPDE Practice Problems:  
  1. Click to HTML Format Copy?
  2. Else, Click to FTP Postscript Copy?
  3. Else, use Anonymous FTP from a terminal window:
     
     ftp babe.math.uic.edu
     "login:" anonymous
     "Password:"
     "ftp>" cd pub/Hanson/MCS571
     "ftp>" get ppp571s97.ps
     "ftp>" quit
• PPDE Computer Problem:  
  1. Click for HTML Format Copy?
  2. Else, Click to FTP Postscript Copy?
  3. Else, Click for Latex Source Copy?
  4. Else, use Anonymous FTP from a terminal window:
     
     ftp babe.math.uic.edu
     "login:" anonymous
     "Password:"
     "ftp>" cd pub/Hanson/MCS571
     "ftp>" get pcp571s97.ps
     "ftp>" quit
  5. Click for Runge-Kutta BC Note Copy?
• PPDE Exam:  
  1. Click to FTP Postscript Copy?
• EPDE Computer Problem:  
  1. Click to FTP Postscript Copy?
• EPDE Practice Problems:  
  1. Click to FTP Postscript Copy?
  2. Else, Click for rough HTML Copy?
• HPDE Practice Problems:  
  1. Click to FTP Postscript Copy?
• Final (EPDE-HPDE) Exam:  
  1. Click to FTP Postscript Copy?