Math 228A - Numerical Solution of Differential Equations

Instructor: J Strain

Lectures: Tuesday and Thursday 11:00-12:30, 70 Evans

Office Hours: Tuesday and Thursday 12:30-2:00, 1099 Evans

GSI: J Kominiarczuk

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

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.
  • Solution of boundary value problems for elliptic systems of linear partial differential equations:
  • Second-order finite difference methods.
  • Derivation and fast solution of boundary integral equations.

    • Grading: Grades will be based on weekly problem sets, some individualized.

    Lecture Notes:

  • Week 01: PDF PS TeX
  • Week 02: PDF PS TeX
  • Week 03: PDF PS TeX
  • Week 04: PDF PS TeX
  • Week 05: PDF PS TeX
  • Week 06: PDF PS TeX
  • Week 07: Notes PDF PS TeX and papers on classical, high-order split, and Krylov-accelerated spectral deferred correction
  • Week 08: PDF PS TeX
  • Week 09: PDF PS TeX
  • Week 10: PDF PS TeX
  • Week 11-12: PDF PS TeX
  • Week 13: PDF PS TeX
  • Week 14: PDF PS TeX
  • Week 15: PDF PS TeX

    • Problem Sets: Please submit to Prof. Strain in 1099 Evans, or send PDFs to strain@math.berkeley.edu

  • Problem Set 01 (due 5 pm, Friday September 4): PDF PS TeX
  • Problem Set 02 (due 5 pm, Thursday September 11): PDF PS TeX
  • A useful handout on the multivariable mean value theorem: PDF
  • Problem Set 03 (due 5 pm, Thursday September 18): PDF PS TeX
  • A C program for demonstrating stiffness stiff.c
  • Problem Set 04 (due 5 pm, Thursday September 25): PDF PS TeX
  • Problem Set 05 (due 5 pm, Thursday October 2): PDF PS TeX
  • Problem Set 06 (due 5 pm, Thursday October 9): PDF PS TeX
  • Problem Set 07 (due 5 pm, Thursday October 23): PDF PS TeX
  • Problem Set 08 (due 5 pm, Thursday November 6): PDF PS TeX
  • Problem Set 09 (due 5 pm, Thursday November 20): PDF PS TeX
  • A matlab/octave program for computing the region of absolute stability ras.m
  • Problem Set 10 (due 5 pm, Thursday December 4): PDF PS TeX
  • A matlab/octave program for computing finite difference weights idwts.m
  • Problem Set 11 (due 5 pm, Thursday December 18 in 1099 Evans): PDF PS TeX