Numerical Methods II

Spring 2006

Instructor: Professor Lisa Fauci
Office: CIMS 525
Phone: (212 998-3191
email: lfauci@cims.nyu.edu

Course Outline

This focus of this course will be numerical methods for both ordinary and partial differential equations. Students should have a good background in the basic theory of ordinary and partial differential equations, aspects of numerical linear algebra, as well as proficiency in a programming language such as Matlab, C or Fortran. There will be thirteen lectures, and my intention is to cover the following topics:

1/23/06 -- Poisson's equation, iterative methods for Ax=b.

1/30/06 -- Iterative methods for Ax=b (conjugate gradient).

2/6/06 -- Polynomial interpolation, quadrature.

2/13/06 -- Initial value problem for ODEs. Euler's method. Consistency, stability, convergence.

2/27/06 -- Multistep methods for ODEs.

3/6/06 -- Runge Kutta methods, absolute stability, stiff ODEs.

3/20/06 -- Newton's method for nonlinear systems.

3/27/06 -- Finite difference methods for parabolic equations. Fourier analysis, stabiility.

4/3/06 -- Parabolic equations in multi-dimensions - ADI method.

4/10/06 -- FFT methods for PDE's.

4/17/06 -- Finite difference methods for advection equations.

4/24/06 -- Finite difference methods for advection equations.

5/1/06 -- A simple finite element method.

Required text

A First Course in the Numerical Analysis of Differential Equations , A. Iserles, published by Cambridge University Press, 1996.

Other useful texts

Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, L.N. Trefethen, 1996. unpublished text, available at http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html .

Numerical Solution of Partial Differential Equations , K.W. Morton, D.F. Mayers, published by Cambridge University Press, 1994.

Introduction to Partial Differential Equations: A Computational Approach , A. Tveito and R. Winther, published by Springer, 1991.


There will be about eight homework assignments during the semester. They will be posted on this page as they are assigned. These assigments will contain both theoretical problems and computational assignments. You may use the computer language of your choice. Your homework should be handed to me in class, or put under my office door. It must be there when I get into my office the morning after the due date.

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6

Assignment 7

Final exam

The final will be an oral exam in my office during the week of May 1, lasting no more that 30 minutes. We will schedule these on an individual basis as we get closer to the end of class.