Spring 2012, Math 6646
Numerical Methods for Ordinary Differential Equations

• Class: MWF 1:05 - 1:55PM
• Classroom: Skiles 268
• Class homepage: http://people.math.gatech.edu/~kang/6646


• Instructor : Sung Ha Kang
  • Email: kang at math.gatech.edu
  • Office: Skiles 247
  • Office hours: WF 2PM - 3PM or my appointment

• the course outline: http://www.math.gatech.edu/course/math/6646


• Prerequisites: Math 2403 and Math 4640


• Course Description: Analysis and implementation of numerical methods for initial and two point boundary value problems for ordinary differential equations

1. (not required) Main Textbook: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by Uri M. Ascher and Linda R. Petzold, SIAM


2. (reference) Numerical Methods for Ordinary Differential Systems: The initial Value Problem by J.D. Lambert, Wiley

• Homework (50%) : Students are strongly encouraged to solve all the homework problems, but only computer homework will be collected (two page limit per question).


• Exams (50%): There will be two exams (one exam and a Final) during the semester which will be based on the homework/lecture materials. No make up exams are allowed. In case of serious illness, doctor's note is required. For excused absences, your adviser's notice is required or the website link showing your participation at the conference, no later than two weeks prior to the date of the exams.

HONOR CODE: All students are expected to comply with the Georgia Tech Honor code. Please review the student code of conduct.

• Jan 18 (Mon) Official School Holiday.
• Ascher&Petzold Chapter 1,2
  Prove Theorem 1.1.
  2.1, (2.4 - in this problem the equation (2.2) means y'=f(t,y).)
• Lambert Chapter 3
  For the first page six examples, show their consistency and zero-stability.
  2.4.1, 2.4.2, 2.5.1, 2.5.2, (2.5.3 just show consistent), 2.5.4, (2.5.5).
• Ascher&Petzold Chapter 3
  3.1, 3.2, 3.3, 3.4, (3.5, 3.8), 3.9, (3.11).
• To hand-in by February 10, 2012 Friday in class: BOLD numbers (posted upto Feb 4th)
  AND THIS HAND-OUT.


• Ascher&Petzold Chapter 4
  (4.4), 4.5, 4.6, (4.7), 4.8, (4.9), 4.11 .
• Lambert Chapter 5
  5.12,1, 5.12,2, 5.3.5, and (ii)
• February 22 (Wed), Exam (in class one hour): upto Runga-Kutta methods


• Ascher&Petzold Chapter 4-1
  4.12 , 4.13, 4.14, (4.15, 4.16),(4.17), 4.19
• Ascher&Petzold Chapter 5
  5.1, 5.2, 5.4, 5.5, 5.6, (5.7), 5.9, 5.10
• Lambert Chapter 3
  3.2.1, 3.2,4, (3.2.5,3,3,4)
• To hand-in by March 14, 2012 Wednesday in class: BOLD numbers (starting with 4.11 to 5.9) ---> POSTPONED to March 16th, 2012 Friday in class.
  Correction THANKS to Carlos: problem 4.11, The value of D has to be 90.5*0.4184e-3 instead of 90.5*0.4814e-3.


• The extra quiz will be posted on T-square on April 2nd (Monday). It is based on multistep methods and predictor-corrector methods. This is a self-administered, one hour, closed book quiz, you can not work with others and should be posted back onto T-square within the given permitted time. (This quiz is extra: extra points will be added, upto 5% of the course grade.)


• Lambert Chapter 4
  4.3.1, 4.3.2, 4.3.4, 4.4.1, 4.4.2.
• Ascher&Petzold Chapter 6
  6.2, 6.3, (6.4).
• Ascher&Petzold Chapter 7
  7.3 , 7.4, 7.6 (a), 7.6 (b).
• Ascher&Petzold Chapter 8
  8.2, 8.3, 8.5, 8.6, 8.7(a), 8.9 , 8.10, 8.11(b).


• To hand-in by April 20, 2012, Friday (optional extension until April 27th Friday). BOLD numbers (starting with 4.3.2 to 8.9)
  


• Optional reading Homework due April 27th, Friday: Read chapter 9 (in particular 9.1 and 9.2), summarize in your own words what DAE is about (at least one page hand-written or half a page typed) and if possible solve exercises 9.2 (and 9.3)). (This homework is extra: extra points will be added, upto 3% of the course grade.)


• April 30 (Mon), 2:50am - 5:40pm FINAL EXAM