MA584 - Numerical Solution of Partial Differential Equations (Fall 2003)

Hours: Class: T, TH 4:05-5:20PM, HA 266.

Instructor:

Dr. Alina Chertock
Office: HA 212
Phone: 515-3200
Office hours: TH 3:00-4:00PM
E-mail: chertock@math.ncsu.edu

Homepage: http://www.math.ncsu.edu/~acherto/NCSU/MA584/584-F03.html

Prerequisites: Calculus I-III, some background in linear algebra, numerical analysis, and ordinary and partial differential equations; Some programming experience (Matlab, Fortran, C, C++, ...)
It is possible to participate in this class without part of the recommended background but this will require you to do a lot of extra reading. Students from all scientific and engineering departments are welcome.

Syllabus: The aim of the course is to provide an introduction to numerical methods for solving partial differential equations of elliptic, parabolic and hyperbolic type. The course will focus on the derivation of methods, on their accuracy, stability and convergence properties, as well as on practical aspects of their efficient implementation. This course should be very useful for students in applied and computational mathematics, and in any area of scientific computing and engineering.

The topics we will cover include:

Fundamentals of finite difference methods.
Consistency, stability, convergence, and error estimates for finite difference methods.
Finite difference methods for elliptic PDE's.
Finite difference methods for parabolic PDE's.
Finite difference methods for hyperbolic PDE's.

Homework #1
Homework #2
Homework #3
Homework #4

Text: A recommended book for this class is

K. W. Morton, D.F Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 2002.

Most of the advanced material is based on recent journal publications. Some books that contain relevant material are:

R. J. LeVeque, Finite Difference Methods for Differential Equations, preprint, 1998.
J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations , Chapman & Hall, 1989.
G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods , Clarendon Press, Oxford, 3rd edition, 1985.
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.
L.C. Evans, Partial Differential Equations, AMS, 1998.
F. John, Partial Differential Equations, Springer-Verlag, 1982.
M.E. Taylor, Partial Differential Equations, Parts I and III, Springer-Verlag.

Grading: There will be a number of homework assignments for this class. Some of the problems will involve programming and you can use any computer language you like. The grading will only be based on homework. No late homework will be accepted. There will be no final exam.

Alina Chertock

Last modified: Mon Nov 24 22:39:43 EST 2003