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| Module Availability |
| Semester 1 and 2 |
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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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2 hour Examination
(Assessment of the following learning outcomes: 1,2,3 and 5.)
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75
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Coursework
Development and testing of a Matlab program to solve Poisson's equation by two different numerical methods.
(Assessment of the following learning outcomes: 4, and, in part 2 and 3.)
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25
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Qualifying Condition(s)
Completion of the progress requirements of Level HE2
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| Module Overview |
| The majority of problems facing Engineers require mathematical models which either do not have analytic solutions for the range of conditions met in practice or, even where they do, are so complex that hand-solution is impractical. Many of these problems can be expressed as partial differential equations. Use of computers to solve problems using approximate numerical methods is thus an every-day part of engineering. This module covers the principles behind a range of methods for both formulating and solving partial differential equations as well as expanding on previous knowledge of solution of algebraic and ordinary differential equations. |
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| Prerequisites/Co-requisites |
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| Module Aims |
To provide a sound understanding of the basic tools available for the numerical solution of a range of partial differential equations encountered by engineers. To familiarize the students with techniques used to design, implement and test numerical solutions. |
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| Learning Outcomes |
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On successful completion of the module you should be able to:
- Describe the basic mathematical ideas behind finite difference, finite volume or finite element techniques.
- Chose an appropriate technique (finite difference or finite element) to solve a common partial differential equation.
- Design an algorithm to solve a common partial differential equation, taking into account appropriate boundary conditions.
- Implement this algorithm in Matlab, including implementing any solution algorithm.
- Analyse the numerical stability of a technique, where appropriate.
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| Module Content |
Polynomial fitting and Taylor's expansion; interpolation and numerical integration (revision).
Solutions off systems of linear equations: Gaussian elimination with partial pivoting, LU factorization and inversion, iterative techniques (Gauss-Seidel, Jacobi, Successive over relaxation).
Finite difference approximations and difference operators. Order and accuracy of approximations.
Application of finite difference approximations to elliptic problems in one and two-dimensions.
Introduction to Finite Element Methods for elliptic problems.
Application of finite difference approximations to parabolic problems in one dimension. Time-stepping methods. Analysis of stability.
Developing codes; validation, testing strategies. |
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| Methods of Teaching/Learning |
22 hours of lectures (11 semester 1, 11 semester 2), 16 hours of tutorial classes (11 semester 1, 5 semester 2), and 62 hours independent learning. 2 hour examination. Tutorials and coursework will include Matlab computer-based exercises.
Total student learning time 100 hours. |
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| Selected Texts/Journals |
Numerical Methods for Engineers, Steven C. Chapra and Raymond P Canale, 2005, McGraw-Hill
Numerical Methods for Mathematics, Science and Engineering, John H. Mathews, 1998, Prentice-Hall
Schaum's Outline of Finite Element Analysis, George R. Buchanan, 1995 |
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| Last Updated |
| 29th September 2010 |
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