MTH 453-553: NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS - Spring 2008
Links
General information
Assignments
General information
Instructor: Malgorzata Peszynska
Class: MWF 10:00-10:50 STAG 132

Course information: CRN 27062. Credits: 3.00.
Student preparation: I expect the students to have a solid background in differential equations and some background/interest in theory and/or applications of partial differential equations.
Prerequisites: students should have taken MTH 256 or equivalent and be currently familiar with ODEs. Having taken one or more of the following classes MTH 480, 481-2, 621-2-3 or similar, 351, 452/552 or similar) is a plus.
Familiarity with (some) numerical methods, algorithms, some programming language, and in particular with MATLAB is a plus.
Having fewer (or none) of the prerequisites does not mean you cannot take the class but it means you (may) have to work hard(er).
Please contact me if you have questions.
Syllabus: In the course we will cover the following topics
  • Review of basic information about numerical solution of differential euqations (very brief).
    Classification of partial differential equations (PDEs), basic PDE models.
  • Finite difference (FD) methods for elliptic BVPs of second order (stationary diffusion)
  • FD methods for heat equation (parabolic IBVPs = nonstationary diffusion).
  • FD methods for first order hyperbolic equation (wave or transport equation: convection or advection problems) and second order wave equation
  • FD methods for equations of mixed type (nonstationary convection diffusion equations)
  • Properties of numerical methods for PDEs: their stability, consistence, convergence, rate of convergence, and cost.
  • Examples of relevant ODEs from applications. You will get computational experience in solving them numerically and enjoy discovering their properties using numerical experiments.
  • Additional topics may include introductory material on nonlinear problems and numerical methods other than FD methods, and solving large sparse linear systems arising from solving stationary diffusion problems.



Textbook:

Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems by Randall J. LeVeque, SIAM, 2007. Paperback: ISBN 978-0-898716-29-0
Exercises and m-files to accompany the book


Enrichment material will be introduced from Numerical analysis for applied science by Myron B. Allen III, Eli L. Isaacson(Wiley, 2005), Numerical Computing with MATLAB by Cleve Moler (SIAM, 2004). Scientific Computing by Michael T. Heath, FD Methods for PDEs by Strikwerda (2004), also from the numerical analysis classic by Stoer and Bulirsch [SB] and from other resources.
MATLAB materials: there exist plenty of good resources for MATLAB, some available online (search, for example, for "matlab tutorial free").

Exams: There will be a Midterm in class on Monday, May 5, and a Final Exam Tuesday, June 10, at 18:00.
Grading: Homework will count as 40% of the grade, exams as 30% each. Additionally, problems for extra credit (for the total up to 10%) will be assigned throughout the term as Homework and/or during Final exam.
Special arrangements for students with disabilities, make-up exams etc.: please contact the instructor and Services for Students with Disabilities, if relevant, and provide appropriate documentation.
Course drop/add information is at http://oregonstate.edu/registrar/.