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General


This course is part of the MAGIC core.

Semester

Autumn 2011 (Monday, October 10 to Friday, December 16)

Timetable
  • Tue 12:05 - 12:55
  • Thu 11:05 - 11:55

Lecturers


Tim Phillips (main contact)
Email PhillipsTN@cardiff.ac.uk
Phone (029) 208 74194
Interests Non-Newtonian fluid mechanics, computational fluid dynamics, numerical analysis
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Photo of Tim Phillips
Andrea Cangiani
Email Andrea.Cangiani@le.ac.uk
Phone (0116) 252 3889
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Photo of Andrea Cangiani


Students


Photo of Azwani  Alias
Azwani Alias
(Loughborough)
Photo of Demetris Avraam
Demetris Avraam
(Liverpool)
Photo of Michael Bennett
Michael Bennett
(Cardiff)
Photo of Matthew Buckley
Matthew Buckley
(Newcastle)
Photo of Mingliang Cheng
Mingliang Cheng
(Manchester)
Photo of Laura Cole
Laura Cole
(Newcastle)
Photo of Tom Croft
Tom Croft
(Cardiff)
Photo of Boris Dadachev
Boris Dadachev
(Cardiff)
Photo of Nina EMBLETON
Nina EMBLETON
(Birmingham)
Photo of Joe Goddard
Joe Goddard
(Keele)
Photo of Esen hanac
Esen hanac
(Birmingham)
Photo of Robert Hicks
Robert Hicks
(Cardiff)
Photo of Akobbet Itoua
Akobbet Itoua
(Liverpool)
Photo of Christopher Jeavons
Christopher Jeavons
(Birmingham)
Photo of Ho Ming Ku
Ho Ming Ku
(Liverpool)
Photo of Juxi Li
Juxi Li
(Leicester)
Photo of Thorpe Maria
Thorpe Maria
(Manchester)
Photo of Laila Naqvi
Laila Naqvi
(Leicester)
Photo of Aniayam  Okrinya
Aniayam Okrinya
(Loughborough)
Photo of Linyu Peng
Linyu Peng
(Surrey)
Photo of Harvind Rai
Harvind Rai
(Birmingham)
Photo of Rahifa Ranom
Rahifa Ranom
(Southampton)
Photo of Yuan Si Cong
Yuan Si Cong
(Manchester)
Photo of Jonathan SIMMONS
Jonathan SIMMONS
(Birmingham)
Photo of Jonathan Stone
Jonathan Stone
(Southampton)
Photo of Desislava Todorova
Desislava Todorova
(Loughborough)
Photo of Michael Walters
Michael Walters
(Cardiff)
Photo of Francis Watson
Francis Watson
(Manchester)
Photo of Chongyuan Xu
Chongyuan Xu
(Liverpool)
Photo of Cyrus Yeadon
Cyrus Yeadon
(Loughborough)


Prerequisites


No prerequisites information is available yet.

Syllabus


1. Introduction and general overview.
2. Approximation Theory. The Fast Fourier transform. 3. Methods for solving systems of linear and nonlinear equations. Gauss elimination, pivoting. Cholesky factorisation. Conditioning and error analysis. Least squares solution, Schur decomposition, the QR and QZ algorithms. Iterative methods: Jacobi, Gauss-Seidel, SOR. The Conjugate Gradient Method. Krylov subspace methods: Arnoldi algorithm. Conjugate gradient method and GMRES.
4. Numerical methods for ODEs. Taylor series methods. Runge-Kutta methods. Multi-step methods. Boundary value problems: shooting methods, finite difference methods, collocation. Methods for conservative and stiff problems.
5. Numerical methods for PDEs. Finite difference methods for elliptic equations. Parabolic equations: explicit, implicit and the Crank-Nicolson methods. The Galerkin, finite element and spectral methods.

Bibliography


An Introduction to Numerical AnalysisE Suli and D Mayers
Theory and Applications of Numerical AnalysisG M Phillips and P J Taylor


Note:

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Assessment


There will be two assessments for this course with each carrying a weight of 50

Assignments


MAGIC066: Numerical Analysis Assessment 1

Files:Exam paper
Deadline: Wednesday 30 November 2011 (1089.9 days ago)


Numerical Analysis - Assessment 2

Files:Exam paper
Deadline: Monday 16 January 2012 (1042.9 days ago)