MTH 453- 553 : NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS - Spring 2013
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General information
Instructor: Malgorzata Peszynska
Class: MWF 10:00-10:50 GLK 115

Course information: Credits: 3.00.
Student preparation: good background in differential equations is required. Experience with and/or interest in partial differential equations are welcome/essential. Familiarity with numerical methods, algorithms, some programming language, and in particular with MATLAB is a plus; however, I will develop the basics as necessary. Students should contact me if their motivation significantly exceeds their preparation so I can suggest how to improve.
Syllabus: In the course we will cover numerical methods for Boundary (BVPs) and Initial Boundary Value Problems (IVPs) for partial differential equations (PDEs) and in particular:
  • Overview of solving differential equations with finite difference methods, and of basic information on partial differential equations.
  • Difference methods for PDEs including all three canonical types of PDEs of second order: elliptic, parabolic, and hyperbolic. Solving first order linear hyperbolic conservation laws.
  • Properties of numerical methods: their stability, consistence, rate of convergence, and cost. You will understand the dilemma between accuracy and efficiency.
  • Examples of applications of PDEs from mechanics, chemistry, biology, and geosciences. Stationary and non-stationary heat conduction and diffusion equations, wave propagation, flow and transport problems. You will get computational experience in solving them numerically and enjoy discovering their properties using numerical experiments.
Additional topics will be developed as time permits: solving numerically PDEs of mixed type, systems, nonlinear problems; an introduction to numerical methods other than finite differences such as finite element method; overview of appropriate algebraic solvers.

Exams: There will be two exams. Exam 1 on May 10 in class. Exam 2 TBA.
Grading: Homework will count as 40% of the grade, exams as 30% each. Problems for extra credit (for the total up to 10%) can/will be assigned individually throughout the term for those interested.

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 from other sources will be used.
MATLAB materials: there exist plenty of good resources for MATLAB, some available online (search, for example, for "matlab tutorial free"). Depending on class needs, we may schedule (some) class(es) in a lab in the first weeks.


Course Outcomes: A successful student will be able to
  • Understand, analyze, and implement basic finite difference schemes for partial differential equations
  • Determine stability and accuracy of an algorithm theoretically and experimentally
  • Propose an appropriate method for a PDE in a given application

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/.