The first aim of this module is to provide the students with both the key theoretical concepts of numerical methods and an insight into practical challenges that arise in the use of these methods.The second aim of this module is to provide the student with the techniques to develop mathematical models of the dynamic behaviour of elements in mechanical systems, including translational, rotational, and fluid systems and systems occurring in automation. The module also aims to enable the student to solve such systems using mathematical and numerical methods. Hence the student will be equipped with the advanced knowledge and practical skills required to evaluate and analyse the behaviour of moderately complex systems.
Computational Preliminaries:
Machine number systems, floating point arithmetic, errors in computation, rounding errors, convergence, use of spreadsheet/programming tools in numerical work.
Solution of Non-linear Equations:
Iteration methods for solution of single non-linear equations, Newton’s method for the solution of nonlinear systems.
Systems Modelling Overview:
Introduction to dynamic systems modelling and simulation methodology, model qualification, model verification, model validation. Classification of variables and systems. Types of models and overview of solution methods.
Fluid systems
Modelling of fluid systems.
Numerical Solution of Differential Equations:
Finite difference solution of O.D.E.’s (single and systems): Runge-Kutta methods.
Translational Mechanical Systems:
Laplace transform solution of 1st and 2nd order models.Variables, element laws, interconnection laws, free body diagrams, parallel and series element combinations, obtaining system models. Solutions using numerical integration and computerised tools.
State-Variable formulation of System Models:
State-variable equations. Input-output Equations. Matrix formulation of state-variable equations. Rotational Mechanical Systems:Variables, element laws, interconnection laws, free body diagrams, obtaining system models.Fluid Systems:Variables, element laws, dynamic models of hydraulic systems. Analysis of solutions using numerical integration and computerised tools.
Interpolation and Approximation theory:
Interpolation by polynomials, cubic splines, Chebyshev and Butterworth polynomials.
Numerical Integration:
Interpolatory numerical integration, Gaussian quadrature, multiple integrals using Monte Carlo methods, error analysis.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |