Numerical Methods II (Chen, Spring 2000)

# Numerical Methods II
G22.2421-001/G63.2020
Graduate Division
Computer Science/Mathematics
Spring 2000

Instructor. Prof. Yu Chen, Warren Weaver Hall (Ciww), Room 1126. Tel: 998-3285, yuchen@cims.nyu.edu

Class mailing list: g22_2421_001_sp00@cs.nyu.edu
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Basic Course Information

Homework and project schedule

Reference for method of deferred corrections
A function for timing in (most) Unix systems

Class Time.
Lecture: 5:10 p.m.-7:00 p.m., Thur., room 102, Warren Weaver Hall (Ciww)
First meeting: Thursday, January 20.
Last day of class: Thursday, April 27.
Spring break: March 13--17; no class on March 16.
Number of lectures: 14

Office hours: 3:00 p.m. - 5:00 p.m. Thursday, and by appointment.

Prerequisite: Numerical Method I, Elements of ODE and PDE.

Important Note: This is computer-programming intensive, but not a programming, course. We assume that you have some experience writing and debugging codes in MATLAB and/or Fortran/C/C++ for the basic tasks discussed in Numerical Methods I. These include matrix factorizations, linear systems solvers, interpolation, approximation, least squares problems, and numerical quadrature. Our goal is to understand the techniques of computational mathematics.

Syllabus: This course will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in actually engaging in scientific computing, rather than addressing theoretical questions in numerical analysis. Computer programming assignments form an essential part of the course homework. We will consider the following topics:

1. Nonlinear equations and Newton's method
2. Ordinary differential equations, Runge-Kutta and multistep methods, convergence and stability
3. Boundary value problems for elliptic equations: finite difference and finite element methods, iterative methods for large scale linear systems of equations as result of discretizing continuous equations
4. Fast solvers, multigrid methods
5. Parabolic and hyperbolic partial differential (time dependent) equations.

Required Text. A first course in the numerical analysis of differential equations, by A. Iserles; available at the university bookstore.

Reference Text.

1. Analysis of numerial methods, E. Isaacson, H. Keller.
2. An introduction to Numerical analysis, G. Strang, G. J. Fix.
3. Numerical methods, G. Dahlquist, A. Bjorck.
4. Introduction to Numerical Analysis, J. Stoer and R. Bulirsch

yuchen@cims.nyu.edu (Yu Chen)
Last modified: March 23, 2000