Math 228A - Numerical Solution of Differential Equations

Lectures: TuTh 11-12:30 am, 75 Evans (Room change effective Thur 18 Sept).

Instructor: J Strain, strain@math.berkeley.edu, 642-3656

Web page: http://math.berkeley.edu/~strain/

Office Hours: Tu 4-6 pm and Th 5-6 pm @ 1099 Evans. Week of Sept 15-20: Tu office hours cancelled due to departmental function. Office hours Wed 4-6, Sept 17, instead.

GSI: Jianlin Xia

Web page (where problem set solutions are posted): http://math.berkeley.edu/~jxia/

Office Hours: TBA

Prerequisites: Math 128A or equivalent. Sufficient computer skills to download, compile and modify numerical packages written in Fortran and C.

Class Notes: Available from the course web page: http://math.berkeley.edu/~strain/228a.F03/

Recommended Texts:

  • E Hairer, SP Norsett and G Wanner, Solving ordinary differential equations, second edition (2 vols.) Springer.
  • UM Ascher, RMM Mattheij, and RD Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM, 1995.
  • P Deuflhard and F Bornemann, Scientific Computing with Ordinary Differential Equations. Springer 2002.

    • Syllabus: The course will cover theory and practical methods for solving systems of one-dimensional differential and integral equations.

  • Methods for solving initial value problems for systems of ordinary differential equations: construction, convergence and implementation:
  • Classical multistep (Adams and BDF) and Runge-Kutta methods
  • Stable high-order deferred correction methods.
  • Solution of boundary value problems for systems of ordinary differential equations:
  • Classical shooting and finite difference techniques.
  • Divide and conquer algorithms for integral equations.

    • Grading: Grades will be based on weekly problem sets and a final project. Project proposals are due Oct 30: design a project related to the course material which will require about the same effort as two homework assignments for you, and write up a 1-page summary of what you will do, why it is related to numerical solution of IVPs or BVPs for ODEs, and how it relates to any larger scientific goals you may have. The final project writeup (about 5-10 pages) is due by Fri Dec 12, 5 pm, at my office or by email...this is a hard deadline!

    Announcements:

  • Nov 25: Office hours canceled today due to dept function. Rescheduled tomorrow, Wed 4-6 pm.
  • Our text for Math 228b next semester will be the two volumes of J. W. Thomas' "Numerical Partial Differential Equations", subtitled "Finite Difference Methods" and "Conservation Laws and Elliptic Equations". They are available through the Springer Yellow Sale at $44.50 each (instead of the usual $64.95), until 31 Dec 2003 or while stocks last.

    • Lecture Notes: (in PostScript format)
  • Week 01, August 26 and 28 PDF PS
  • Week 02, September 3 and 5 PDF PS
  • Week 03, September 9 and 11 PDF PS
  • Week 04, September 16 and 18 PDF PS
  • Week 05, September 23 and 25 PDF PS
  • Week 06, September 30 and October 2 PDF PS
  • Weeks 07 and 08, October 7 through 16 PDF PS
  • Week 09, October 21 through 23 PDF PS
  • Week 10, October 28 through 30 PDF PS Our text for this week and next is here: PDF PS
  • Week 11, November 4 and 6 PDF PS
  • Week 12, November 13 PDF PS
  • Week 13, November 18 and 20 PDF PS
  • Week 14 and 15, November 25 through Dec 4 PDF PS Our text for this week and next is here: PDF PS

    • Problem Sets:

  • Problem Set 1: Solve the exercises in the notes for Week 01 and hand in Thursday Sep 4 in class.
  • Problem Set 2: Solve the exercises in the notes for Week 02 and hand in Thursday Sep 11 in class. Download stiff.c here.
  • Problem Set 3: Solve the exercises in the notes for Week 03 and hand in Thursday Sep 18 in class.
  • Problem Set 4: Solve the exercises in the notes for Week 04 and hand in Thursday Sep 25 in class.
  • Problem Set 5: Solve the exercises in the notes for Week 05 and hand in Thursday Oct 2 in class.
  • Problem Set 6: Solve the exercises in the notes for Week 06 and hand in Thursday Oct 9 in class.
  • Problem Set 7: Solve the exercises in the notes for Weeks 07 and 08 and hand in Thursday Oct 23 in class. Download ras.m here.
  • Problem Set 8: Solve the exercises in the notes for Week 09 and hand in Thursday Oct 30 in class. (Note 1-2 page project proposals are also due Oct 30.)
  • Problem Set 9: Solve the exercises in the notes for Week 10 and hand in Thursday Nov 6 in class.
  • Problem Set 10: Solve the exercises in the notes for Week 11 and hand in Thursday Nov 20 in class.
  • Problem Set 11: Solve the exercises in the notes for Week 12 and hand in Thursday Nov 27 in class.
  • Problem Set 12: Solve the exercises in the notes for Week 13 and hand in Thursday Dec 4 at the last class. Find the code idwts.m here.