Math 269 A

Math 269 A: Advanced Numerical Methods
MS 6229, MWF, 1-1:50 PM
Professor: Joseph Teran
Office: MS 7619E
Office hours: MW, 2-3

Summary

We will cover finite difference methods for systems of ordinary differential equations. We will investigate convergence behavior numerically and analytically.
The required text for the course is:

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, by Ascher and Petzold.

Notes and Handouts

Stability of ODE systems.
Multistep Methods I.
Runge-Kutta.
Multistep Methods II.
Boundary Value Problems.
Finite Differences I.
Finite Differences II.
Shooting Methods Intro.
Shooting: Elasticity Problem.
Shooting: Uniqueness.
Shooting: Newton Convergence.
Discontinuous Solutions.
Steady State Burger's: Intro.
Characteristics and Burger's.
Riemann and Burger's.
Finite Differences and Steady State Burger's.
Discrete Duhamel's Principle.

Assignments

There will be three homework assignments with equal weight. The work will require some programming (Matlab will be fine) and there will also be some pen and paper problems. There will also be a final exam.

Homework 1, Due October 28.
Homeworks 2 and 3, Due December 12.