Lectures: TuTh 9:30-11 am, 81 Evans

Course Control Number: 55227

Instructor: J Strain, strain@math.berkeley.edu

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

Office Hours: Tu 2-4 pm and Th 2-3 pm @ 1099 Evans. Finals weeks: Monday and Friday December 10 and 14, 4-6 pm. *All problem sets should be handed in by Friday December 14.*

GSI: A Rangan, rangan@math.berkeley.edu

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

Office Hours: 3-5 pm Wed & Th @ 1057 Evans.

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://www.math.berkeley.edu/~strain/228a.F01/

Recommended Texts:

• E Hairer, SP Norsett and G Wanner, Solving ordinary differential equations, second edition (2 vols.) Springer, 1993 and 1996.
• UM Ascher, RMM Mattheij, and RD Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM, 1995.

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.

Lecture Notes: (in PostScript format)

• Lecture 01, August 28
• Lecture 02, August 30
• Lecture 03, Sep 4
• Lecture 04, Sep 6
• Lecture 05, Sep 11
• Lecture 06, Sep 13
• Lecture 07, Sep 18
• Lecture 08, Sep 20 (updated Sep 24) (An interesting example of the design of Runge-Kutta methods for tailored regions of absolute stability rather than order: Sommeijer et al, 1997. )
• Lecture 09, Sep 25
• Lecture 10, Sep 27
• Lecture 11, Oct 2
• Lecture 12, Oct 4
• Lecture 13, Oct 9 (Paul Griffiths has kindly provided a C program and executable for timing programs under Windows 2000 and NT: Description Executable Source code )
• Lecture 14, Oct 11
• Lecture 15, Oct 16
• Lecture 16, Oct 18
• Lecture 17, Oct 23
• Lecture 18, Oct 25
• Lecture 19, Oct 30 Updated Nov 6---corrected van der Pol equation!
• Lecture 20, Nov 1 The Starr-Rokhlin technical report [SR94] is available here: PDF PS
• Lecture 21, Nov 6 (Revised Nov 7)
• Lecture 22, Nov 8 (Revised Nov 7)
• Lecture 23, Nov 13 A matlab script for computing interpolation and differentiation weights is here .
• Lecture 24, Nov 15 (Updated Nov 14)
• Lecture 25, Nov 20
• Lecture 26, Nov 27
• Lecture 27, Nov 29
• Lecture 28, Dec 4 : The fast Gauss transform (L. Greengard and J. Strain, SIAM J. Sci. Stat. Comput. 12 (1991), 79-94.)
• Lecture 29, Dec 6 : Fast spectrally-accurate methods for variable-coefficient elliptic problems (J. Strain, Proc. of the AMS. 122 (1994), 843-850.)

Problem Sets: *All problem sets should be handed in by Friday December 14.*

• Problem Set 1: Solve the exercises in Lectures 01 and 02 and hand in Thursday Sep 6 in class.
• Problem Set 2: Solve the exercises in Lectures 03 and 04 and hand in Thursday Sep 13 in class. stiff.c
• Problem Set 3: Solve the exercises in Lectures 05 and 06 and hand in Thursday Sep 20 in class.
• Problem Set 4: Solve the exercises in Lectures 07 and 08 (updated Sep 24 to omit the last few exercises) and hand in Thursday Sep 27 in class.
• Problem Set 5: Solve the exercises in Lectures 09 and 10 and hand in Thursday Oct 4 in class.
• Problem Set 6: Solve the exercises in Lectures 11 and 12 and hand in Thursday Oct 11 in class.
• Problem Set 7: Solve the exercises in Lectures 13 and 14 and hand in Thursday Oct 18 in class. ras.m
• Problem Set 8: Solve the exercises in Lectures 15 and 16 and hand in Thursday Oct 25 in class.
• Problem Set 9: Solve the exercises in Lectures 17 and 18 and hand in Thursday Nov 1 in class.
• Problem Set 10: Solve the exercises in Lectures 19 and 20 and hand in Thursday Nov 8 in class.
• Problem Set 11: Solve the exercises in Lectures 21 and 22 and hand in Thursday Nov 15 in class.
• Check your results if you like by downloading the Legendre zeros Z on [-1,1], weights W on [-1,1] and spectral integration matrix S on [0,1] here: the matrix S on [t,t+h] is this one multiplied by h. Z_004 Z_008 Z_016 Z_024 Z_032 Z_040 Z_048 Z_056 Z_064 Z_072 Z_080 Z_088 Z_096 Z_104 Z_112 Z_120 Z_128 W_004 W_008 W_016 W_024 W_032 W_040 W_048 W_056 W_064 W_072 W_080 W_088 W_096 W_104 W_112 W_120 W_128 S_004 S_008 S_016 S_024 S_032 S_040 S_048 S_056 S_064 S_072 S_080 S_088 S_096 S_104 S_112 S_120 S_128
• Problem Set 12: Solve the exercise in Lecture 23 and hand in Tuesday Nov 27 in class.
• Problem Set 13: Solve the exercise in Lecture 24 and hand in Thursday Dec 6 in class.