This page will contain some information about the Winter 2010/2011 MAT 1508 course
on Techniques of Applied Math: Introductory Numerical Methods for Differential Equations .
Course official website on the Blackboard:
MAT 1508HS
TECHNIQUES OF APPLIED MATH: INTRODUCTORY NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
Course outline:
The course will focus on finite difference and spectral methods (Galerkin method, the tau method, the collocation method) for ordinary and partial differential equations (parabolic, hyperbolic and elliptic) with partial emphasis on theoretical aspects, such as error and stability analysis. The presented material will be illustrated by examples from mathematical physics and samples of Matlab codes will be provided. Review of weak formulations of ODEs and PDEs problems will be given but knowledge of ODEs and PDEs at an introductory undergraduate level is required for the course.
List of topics that we will discuss:
- Finite difference schemes.
- Analysis (accuracy, consistancy, conservation properties, convergence) of finite-difference schemes for BVP (ODE)
- Analysis (accuracy, consistency, conservation properties, convergence and stability) of finite-difference schemes for IVP (ODE)
- Analysis (accuracy, consistency, conservation properties, convergence and stability) of finite-difference schemes for different types of PDEs
- Approximation theory. Spectral methods. Pseudo-spectral methods.
- Applications of spectral and pseudo-spectral methods to ODE and to PDE
- Wavelets
Location and time:
We meet in HU1018 (215 Huron str. building) Tuesdays 4pm – 6pm, (6pm – 7pm CQUEST LAB. 107)
Marking Scheme:
40% from the homework that is assigned every week but with a due date in two weeks and 60% from the individual project that will require a 15-20 minutes presentation and an implementation of some numerical methods using a programming language of your choice. List of projects will be posted.
Main references:
1. “Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations” by Lloyd N. Trefethen free on-line version is here:
https://people.maths.ox.ac.uk/trefethen/pdetext.html
2. “Chebyshev and Fourier Spectral Methods” by J. P. Boyd free on-line version is here:
http://www-personal.umich.edu/~jpboyd/BOOK_Spectral2000.html
Additional references:
1. Spectral Methods in Matlab/ Lloyd N. Trefethen
2. Numerical Mathematics/ M. Grasselli, D. Pelinovsky