CO906 Numerical Simulation of Continuous Systems
This module will not run in 201213
Module Leader: Dr Colm Connaughton (Mathematics and Complexity)
link to Online Course Materials
Taken by students from:
Code  Degree Title  Year of study  core or option  credits 
PF3P4(5) 
Complexity Science MSc (+PhD) 
1 
option 
12 
PG1P8(9) 
Complexity Science MSc (+PhD) 
1 
option 
12 
PG3G1  Maths and Stats MSc (+PhD)  1  option  12 
PF3P6(7)  MSc in Complex Systems Science  1 or 2  option  12 
Context: This is part of of the Complexity DTC taught programme.
Module Aims:
The module covers computational methods for solving partial differential equations with an emphasis problem solving and applications in Complexity Science.
Syllabus:

Basic theory of ordinary differential equations and their numerical solution
 initial and boundary value problems, dynamical systems
 approximation of derivatives via finite differences, error analysis
 Euler and predictorcorrector methods
 RungeKutta methods
 Stiffness, instability and singularities
 Applications: PredatorPrey models, chaotic dynamics.

Partial differential equations (PDE’s)
 classification of PDE’s as elliptic, parabolic or hyperbolic
 Nondimensionalisation and similarity solutions
 first order PDE’s and the Method of Characteristics
 Applications: traffic flow models

Numerical Solution of Parabolic PDE’s
 Finite difference approximation of the heat equation and explicit Euler method
 Explicit vs implicit timestepping, stability and the CrankNicholson method
 Applications: BlackScholes equation, FokkerPlanck equation

Numerical Solution of Hyperbolic PDE’s
 Explicit methods and CFL criterion
 Implicit methods for second order equations
 Conservation laws and LaxWendroff schemes
 Applications: Telegraph Equation

Spectral Methods
 Fast Fourier Transform
 Spectral and Pseudospectral methods
 Applications: Nonlinear Schrodinger Equation
 Fast Fourier Transform
Illustrative Bibliography:
 J.M. Cooper: Introduction to Partial Differential Equations with MATLAB
 T. Pang: An Introduction to Computational Physics
 W. F. Ames: Numerical Methods for Partial Differential Equations
 Printed lecture notes will also be provided.
Teaching:

Lectures per week
2 x 1 hours
Classwork sessions per week
2 x 1 hours
Module duration
10 weeks
Total contact hours
40
Private study and group working
80
Assessment information 2011:
Week 
Assessment 
Issued 
Deadline 
how assessed 
%credit 
1 
Problem sheet #1 
110111 
310111 12:00 
written script 
15 
4  Problem sheet #2  010211  210211 12:00  written script  20 
7 
Problem sheet #3 
220211 
140311 12:00 
written script 
15 
10 
Oral Examination 
150311 
Oral examination 
50 