MATH 649 (04779), Spring 2009

Numerical Analysis: Differential Equations

Catalog Description:
In-depth treatment of numerical methods for ordinary differential equations; introduction to methods for partial differential equations.
Desired Learning Outcomes:
Students will be able to:
  • Utilize numerical algorithms for solving differential equations.
  • Analyze the convergence, stability, accuracy, and efficiency of such algorithms.
  • Prove the fundamental theorems upon which such analysis is based.
  • Prerequisites:
    MATH 544 and (541 or 549 or 645A)
    Instructor:
    Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
    Office hours: Monday 9:10-10am, Tuesday 9:10-10am, Thursday 9:10-10am, and Friday 9:10-10am.
    Web page:
    http://www.ohio.edu/people/mohlenka/20093/649.
    Class hours/ location:
    MTuThF 12:10-12m in 313 Morton Hall.
    Text:
    A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback), by Arieh Iserles; Cambridge University Press; 2nd edition (December 29, 2008) ISBN-10: 0521734908, ISBN-13: 978-0521734905.
    Homework:
    There are relatively few homework problems in the book, so we will attempt to do the majority of them. To build your mathematical writing skills: The exact problem numbers and due dates will be announced as we go.
    Project:
    You will do a written report and give a presentation on a project such as:
    Tests:
    There will be one mid-term test, in class.
    Final Exam:
    The final exam is on Friday, June 12, at 12:40pm in our regular classroom.
    Grade:
    Your grade is based on homework 50%, test 15%, final exam 20%, and project 15%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-. Grades are not the point.
    Attendance:
    Attendance and participation is very important in this course, since the learning model is based on group in-class activities. I do not count attendance in your grade, since absences will penalize you through your loss of learning.
    Academic Dishonesty:
    On the homework you may use any help that you can find, but you must acknowledge in writing what help you received and from whom or where. The test and final exam must be your own work, and without the aid of notes, etc. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
    Special Needs:
    If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
    Learning Resources:
  • Your classmates are your best resource. Use them!
  • LaTeX, Python, and Matlab resources.
  • Schedule

    Subject to change.
    Week Date Topic/Materials Skill/Homework/Test
    Text Other
    1 March 30 Introduction
    1: Euler's method and beyond
    March 31 1.1 Numerical ordinary differential equations; Lipschitz continuity read chapter 1
    April 2 1.2 Euler method Mathematical autobiography due
    April 3 1.3 homework problem numbers to be announced
    2 April 6 1.4
    2: Multistep methods
    April 7 2.1 Linear multistep method read chapter 2
    April 9 2.2
    April 10 2.3 Layout skill starts
    3 April 13 (drop deadline)
    3: Runge-Kutta methods
    April 14 3.1 Runge-Kutta methods; Gaussian quadrature read chapter 3
    April 16 3.2 Explicit and implicit methods
    April 17 3.3 Flow skill starts
    4 April 20 3.4
    April 21
    4: Stiff equations
    April 23 4.1 Stiff equation read chapter 4
    April 24 4.2 Logic skill starts
    5 April 27 4.3
    April 28 4.4
    April 30 Review
    May 1 Test on Chapters 1-4
    8: Finite difference schemes
    6 May 4 8.1 Poisson's equation; Discrete Poisson equation; Finite difference read chapter 8 (drop deadline with WP/WF)
    May 5 8.2
    May 7 8.3
    May 8 Intros skill starts
    16: The diffusion equation
    7 May 11 16.1 Diffusion equation read sections 16.1-3
    May 12 16.2
    May 14 16.3 read sections 16.4-6
    May 15 16.4 Symbols skill starts
    8 May 18 16.5
    May 19 16.6 Project outline due
    17: Hyperbolic equations
    May 21 17.1 Hyperbolic partial differential equation; Advection read sections 17.1-3
    May 22 17.2 Graphs skill starts
    9 May 25 Memorial Day, no class
    May 26 17.3 read sections 17.4-5
    May 28 17.4 Wave equation
    May 29 17.5 Burgers' equation
    10 June 1 Project presentations
    June 2 Project presentations
    June 4 Project presentations
    June 5 Review Project reports due
    11 June 12 Friday, 12:40pm in our regular classroom Final Exam

    Martin J. Mohlenkamp
    Last modified: Fri Sep 3 13:54:36 EDT 2010