Math 228A - Numerical Solution of Differential Equations

Lectures: TuTh 2-3:30 pm, 75 Evans (9 Evans from 14 September onward).

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

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

GSI: Yossi Farjoun

Web page (where problem set solutions will be posted): http://math.berkeley.edu/~yfarjoun/

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

Class Notes: Available from the course web page: http://math.berkeley.edu/~strain/228a.F04/

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 initial value problems for systems of ordinary differential-algebraic equations.
  • 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 Nov 16: design a project related to the course material which should require about two to three weeks effort 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 Wed Dec 15, 5 pm, at my office or by email...this is a hard deadline!

    Lecture Notes:

  • Week 01, Aug 31 and Sept 2 PDF PS
  • Week 02, Sept 7 and 9 PDF PS
  • Week 03, Sept 14 and 16 PDF PS
  • Week 04, Sept 21 and 23 PDF PS
  • Week 05, Sept 28 and 30 PDF PS
  • Week 06, Oct 5 and 7 PDF PS
  • Week 07, Oct 12 and 14 PDF PS
  • Week 08, Oct 19 and 21 PDF PS
  • Week 09, Oct 26 and 28 PDF PS. A useful reference for spectral deferred correction is the original preprint, here in PDF and PS formats.
  • Weeks 10 and 11, Nov 2, 4 and 9 PDF PS Here is a preprint on deferred correction methods, in PDF and PS formats.
  • Weeks 12 and 13, Nov 16, 18 and 23 PDF PS Here is a preprint on integral equation methods, in PDF and PS formats.
  • Week 14, Nov 30 and Dec 2 PDF PS
  • Week 15, Dec 7 and 9 PDF PS

    • Problem Sets:

  • Problem Set 1: Solve Exercises 1-9 in the lecture notes for week 01, and hand in Thursday Sep 9 in class.
  • Problem Set 2: Solve Exercises 1-7 in the lecture notes for week 02, and hand in Thursday Sep 16 in class. Here is program stiff.c.
  • Problem Set 3: Solve Exercises 1-4 in the lecture notes for week 03, and hand in Thursday Sep 23 in class.
  • Problem Set 4: Solve Exercises 1-3 in the lecture notes for week 04, and hand in Thursday Sep 30 in class.
  • Problem Set 5: Solve Exercises 1-6 in the lecture notes for week 05, and hand in Thursday Oct 7 in class.
  • Problem Set 6: Solve Exercises 1-4 in the lecture notes for week 06, and hand in Thursday Oct 14 in class.
  • Problem Set 7: Solve Exercises 1-3 in the lecture notes for week 07, and hand in Thursday Oct 21 in class. Here is the Matlab script ras.m for exercise 3.
  • Problem Set 8: Solve Exercises 1-2 in the lecture notes for week 08, and hand in Thursday Oct 28 in class.
  • Problem Set 9: Solve Exercises 1-6 in the lecture notes for week 09, and hand in Tuesday Nov 9 in class.
  • Problem Set 10: Solve Exercises 1-6 in the lecture notes for week 10-11, and hand in Thursday Nov 18 in class.
  • Problem Set 11: Solve Exercise 1 in the lecture notes for week 12-13, and hand in Thursday Dec 2 in class. Here is the Matlab script idwts.m for exercise 1.