Numerical solution of partial differential equations
MTH 453/553

MWF 10:00-10:50
MLM 234
Spring 2015

Professor:

Dr. Nathan Louis Gibson  

Office:

Kidd 312

Office Hours:

MF 11-11:50

Course Website:  

http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH553-001S15

Text Book
(for 552 and 553):

Randy LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM (SIAM Member discount: contact me if you are not yet a member..membership is free to all OSU students!)

Course Description

This course will explore numerical methods based on finite difference discretizations for solving partial differential equations (PDEs), including time dependent. Partial differential equations are used to describe a large variety of physical phenomenon, from fluid flow to electromagnetic fields. They also arise in many diverse applications as ecology, mechanical systems, earth sciences and mathematical finance.

A derivation of methods appropriate for particular classes of PDEs will be presented. We will focus on analysis of stability, accuracy, convergence, and implementation of these methods. Students will get computationalexperience in applying the algorithms studied using the MATLAB problem-solving environment. We will also discuss techniques particularly efficient in solving linear systems arising from implicit discretizations of PDEs, and contrast finite difference and finite element methods, as time permits.

Prerequisites: Familiarity with basic properties of differential equations (MTH 256) and matrices (MTH 341 or 306), and some programming experience (preferably with MATLAB) is required. Familiarity with PDEs is a plus; however we will develop the basics as necessary. Those who have taken the equivalent of MTH452/552 would be well-prepared. Students who are not sure about prerequisites are encouraged to talk to me.

Matlab

The programming language for this course is MATLAB. Oregon State University has subscribed to a Total Academic Headcount (TAH) Site License for MATLAB. This new licensing includes many, but not all MATLAB toolboxes. OSU faculty, staff and students can install on up to 4 personally-owned devices or computers. For more information visit Information Services -- MATLAB.

  • Some tutorials:

    Grades

    Grade Distribution

    Homework 40%
    Midterm 30%*
    Final 30%
    Total 100%

    *Note: Final exam grade will replace midterm grade if higher.

    Grade Scale

    A 93
    A- 90
    B+ 87
    B 83
    B- 80
    C+ 77
    C 73
    C- 70
    D+ 67
    D 63
    D- 60

    Homework

    Homework assignments will be posted here as pdf files. They will be mostly self-contained, but possibly referencing methods or equations from the text. Some problems will require programming and/or computational experimentation. This is not a programming course, thus many algorithms will be coded for you. However, you will need to know how to fix, modify and use MATLAB codes.

    Assignments should be completed individually. You may confer with fellow students in general terms, but must write code and solutions on your own.

    If your homework is late you will receive up to half credit for the first two days after the due date. Homework submitted three days or later after the due date will not receive any credit.

    553: denotes a problem that is required only for students enrolled in MTH 553, but can serve as extra credit for MTH 453 students.
    453: denotes a problem that is optional for MTH 553 students.

    There will be approximately four assignments to be posted here and on Blackboard.

    Exams

    There will be one midterm exam on Monday May 4, and one cummulative final exam Monday Jun 8 at 2PM.

    Links

    Last updated: Fri Jun 05 09:55:17 PDT 2015