Department of Mechanical Engineering, Unit Catalogue 2006/07 |
ME20014 Modelling techniques 1 |
Credits: 6 |
Level: Intermediate |
Semester: 1 |
Assessment: EX60CW40 |
Requisites: |
Aims:
* To continue to develop algorithm design and programming techniques in C++. * To acquire a large variety of numerical and mathematical techniques to be used for those engineering problems modelled in terms of ODEs. * To provide a strong mathematical and computational foundation for solving equations arising in the modelling of engineering systems. Learning Outcomes: After taking this unit the student should be able to: * Understand how the various standard ordinary differential equations (ODEs) arise in engineering. * Understand and use numerical techniques in the solution of such ODEs. * Understand and apply the techniques of Fourier series and Laplace transforms to ODEs. * Understand the use of object orientation and its relation to C++ classes. Skills: Problem solving; numeracy; working independently. Content: Numerical solution of ordinary differential evolution equations using Euler's method and the Runge-Kutta methods, including reduction to first order form and numerical stability analysis. Numerical solution of two-point ordinary differential boundary value problems using a direct method (the tridiagonal matrix algorithm and an indirect method (the shooting method). Local and Global Truncation Errors: choosing a suitable numerical method and the improvement of accuracy. Translating engineering problem statements in English into ODEs, and hence into C++ software. C++ classes, private and public member data and functions, constructors and destructors and their relationship with memory management, data hiding, and Fourier Series and Laplace transforms. |
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