Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Numerical Solution of PDEs
Module Code	MS401
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Eugene O'Riordan Semester 2: Eugene O'Riordan Autumn: Eugene O'Riordan
Module Teacher	Eugene O'Riordan
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

The course considers both the practical and the theoretical issues associated with solving partial differential equations using numerical methods. The continuous assessment is a computational project, which involves implementing the numerical methods discussed in the lectures. The course develops skills in constructing mathematical proofs for the theorems involved in the associated numerical analysis.

Learning Outcomes

1. Prove theorems establishing a comparison principle for both elliptic and parabolic differential operators
2. Solve some theoretical problems associated with the iterative solution of a linear system of equations
3. Explain arguments used to prove selected theorems from the course
4. Use appropriate software to implement the theoretical algorithms analysed in the lectures, assess the performance of these algorithms and present a written report based on the numerical experiments

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	3	No Description
Laboratory	1	Computer Lab Tutorial
Independent learning time	4	No Description
Total Workload: 8

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

ITERATIVE SOLUTION OF LARGE SPARSE SYSTEMS OF EQUATIONS.
Review of direct methods.LU-decomposition. Ill-conditioned matrices. Iterative Methods. Jacobi, Gauss-Seidel and SOR. Conjugate-gradient methods. Theoretical convergence results..

APPLICATIONS TO FINITE DIFFERENCE METHODS FOR P.D.E.S.
Stability, Discrete Maximum Principle. M-matrices and monotonicity. Upwinding. Singularly perturbed problems..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Project	n/a	25%	Week 11

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

Axelsson:: 1996, Iterative solution methods,
Strikwerda,: 1989, Finite Difference Schemes and Partial Differential Equations,
Smith: 1985, Numerical solution of partial differential equations,
Quarteroni, Sacco and Saleri: 2000, Numerical Mathematics, Springer,

Other Resources

None

Array

Programme or List of Programmes

APM

B.Sc. Applicable Mathematics

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

ECSA

Study Abroad (Engineering & Computing)