Description:
| Aims: To continue to develop algorithm design and programming techniques in MATLAB.
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 the use of computer programming using MATLAB for the solution of engineering problems described by ODEs.
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 MATLAB software.
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