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This is the archived MA500-1 web page from 2014/2015.
If you are looking for the page for the current academic year, please see nuigalway.blackboard.com, or contact the module's lecturer.

MA500-1: Numerical Differential Equations

Course Information

Lecturer:	Dr Niall Madden
Lectures:	Monday at 11.00 Tuesday at 11.00 Wednesday at 12.00 Classes take place in ADB-1020.
Starts:	Monday, Sep 8, at 11.00.
Lecture summaries:	see below.
Credits:	10 ECTS (a 5 ECTS variant may be available to students in structured PhD programmes).
Overview:	This module is concerned with the mathematics of algorithms for the numerical solution of differential equations, mainly by finite different methods. It is aimed at graduate students (taught Masters and structured PhD programmes) in mathematical and computational sciences.

Details

Except in very rare cases, it is not possible to solve differential equations by apolitical methods. The best one can do is generate approximate solutions using numerical algorithms. In this module, we mainly focus on the use of finite difference methods for ordinary and partial differential equations. The construction/derivation of these methods will be our initial focus. However, most of the effort will go into analysing the methods, and establishing rigorous error bounds. We'll also study their implementation in Matlab, though this will be mainly in support of our theoretical studies.

Texts:

Through the semester, I'll use various texts. As I introduce a text, the details will be added below. Some of these are published by SIAM and are freely available to you on-line through NUI Galway's subscription to SIAM e-books.

Randall J. Levesque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems
John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Second Edition

The following books are useful if you are trying to learn the basics of Matlab.

Tobin A. Driscoll, Learning MATLAB. (620.00151 DRI).
Cleve B. Moler, Numerical Computing with Matlab.
Desmond J. Higham and Nicholas J. Higham, Matlab Guide: Second Edition. (518.0285 HIG)

Lecture Summaries

These are extremely brief accounts of what was discussed in class at each lecture. Please refer to your lecture notes.

Lecture 1:	Welcome to the Masters Programme, and to MA500-1	11am, Monday, 08/09/14
Lecture 2:	Approximation of derivatives	11am, Tuesday, 09/09/14
Lecture 3:	Taylor's series	12pm, Wednesday, 10/09/14
Lecture 4:	Introduction to finite difference methods	11am, Monday, 15/09/14
Lecture 5:	Towards error analysis	11am, Tuesday, 16/09/14	Code: SimpleFD1.m
Lecture 6:	Error analysis: Part 1	12pm, Wednesday, 17/09/14
Lecture 7:	Norms (i)	11am, Monday, 22/09/14	Lecture notes
Lecture 8:	Norms (ii): norms of matrices	11am, Tuesday, 23/09/14	Lecture notes
Class 9:	More norms	12pm, Wednesday, 24/09/14
Class 10:	Finite differences in Matlab (1).	11am, Thursday, 25/09/14	Class notes Code: Solve_FD.m Code: Test_FD.m
Class 11:	Consistency + Stability ⇒ Convergence	11am, Monday, 29/09/14
Class 12:	Convergence in the 2-norm	11am, Tuesday, 30/09/14
Class 13:	Convergence in the max-norm	12pm, Wednesday, 01/10/14
Class 14:	Maximum principles for differential equations	11am, Monday, 06/10/14
Class 15:	Maximum principles for difference equations	11am, Tuesday, 07/10/14
Class 16:	Neumann boundary conditions (1)	12pm, Wednesday, 08/10/14
Class 17:	Neumann boundary conditions (2)	11am, Monday, 13/10/14
Class 18:	General boundary value problems	11am, Tuesday, 14/10/14
Class 19:	More on general BVPs	12pm, Wednesday, 15/10/14
Class 20:	Elliptic BVPs in two dimensions	11am, Monday, 20/10/14
Class 21:	A simple FEM for the Poisson problem	11am, Tuesday, 21/10/14
Class 22:	Ordering the unknowns in a 2D FEM	12pm, Wednesday, 22/10/14
Class 23:	Expressing finite difference methods using Kronecker products	11am, Tuesday, 28/10/14
	Problem Set 2
	Brief details of each class.

School of Mathematics, Statistics and Applied Mathematics
National University of Ireland, Galway, University Road, Galway, Ireland.
Phone: +353 (0)91 492332 (direct) , +353 (0)91 524411 x2332 (switchboard)
Fax: +353 (0)91 494542 Email: Mary.Kelly@nuigalway.ie
This page was last updated Friday, September 04