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| Module Availability |
Spring Semester. |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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50 minute class test
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10
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MATLAB coursework
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15
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Exam
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75
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Qualifying Condition(s)
A aggregate mark of 40% is required to pass this module.
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| Module Overview |
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Cannot be easily solved by hand and computational techniques play an important role in understanding and interpreting the behaviour of a given PDE.
In this module we examine some numerical methods for solving PDEs including the theory that underlies them and their application.
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| Prerequisites/Co-requisites |
MAT2001 Numerical and Computational Methods
MAT2011 Linear PDEs |
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| Module Aims |
The aim of the module is to introduce the basic principles behind applying finite difference methods to solve elliptic, parabolic and hyperbolic partial differential equations and finite element methods to elliptic partial differential equations.
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| Learning Outcomes |
By the end of the course students should
* know how to apply some numerical methods to solve partial differential equations
* be able to write MATLAB code to solve simple cases.
* understand the notions of convergence, accuracy and stability for the methods that they learn. |
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| Module Content |
* Finite differences methods in general, there derivation and the notions of accuracy, consistency and stability.
* Specific finite difference methods for parabolic partial differential equations including Euler's method, the theta method and the Crank-Nicolson method.
* Specific finite difference methods for hyperbolic partial differential equations including upwind schemes, the leapfrog method and the Lax Wendroff method. The Lax Equivalence Theorem will be discussed.
* Finite element methods for elliptic partial differential equations.
* An important part of the course will be the hands on experience of writing and running code to solve partial differential equations. For this purpose MATLAB will be used and the basics of how to use MATLAB will be taught. |
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| Methods of Teaching/Learning |
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Teaching is by lectures, tutorials and computer laboratory sessions. Learning takes place through the lectures, reading through lecture notes and textbooks, tutorials, working through example sheets and the computing laboratory sheets.
3 lectures/tutorial hours per week. At least one of these sessions every fortnight will be held in a computing laboratory.
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| Selected Texts/Journals |
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G.D. Smith, Numerical Solution of Partial Differential Equations, OUP 2003.
R.L. Burden and J.D. Faires, Numerical Analysis, Brooks/Cole 2001.
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| Last Updated |
04.11.08 |
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