Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering – Stage 2
Bachelor of Engineering in Mechanical Engineering – Stage 2
(NFQ – Level 8)
Autumn 2005
Computing and Numerical Analysis
(Time: 3 Hours)
Instructions
Answer any FOUR questions.
All questions carry equal marks.
Examiners: Dr. R. Sheehy
Mr. J. E. Hegarty
Prof. J. Monaghan
Q1. (a) Describe the Gauss Elimination Method for solving a system of linear equations. (9 marks)
(b) Write a program which uses the Gauss Elimination Method with partial pivoting for
solving a system of linear equations. (10 marks)
(c) Briefly describe the main pitfalls in using Gauss Elimination and list some techniques for
improving the solution. (6 marks)
Q2. (a) Describe any two of the following methods for obtaining roots of an equation:
(i) Newton – Raphson
(ii) Bisection
(iii) False – Position (6 marks)
(b) Explain the terms convergence and stability as applied to numerical methods for
obtaining roots and show that
(
)
(
)
()()
2
.
xf
xfxf
′
′< 1 is a necessary condition for
convergence of Newton – Raphson Method. (8 marks)
(c) Outline the general structure of a program for locating single roots of an Equation.
(6 marks)
(d) The displacement of a structure is defined by y = 10e0.5t Cos2t for damped oscillation.
Estimate the time required for the displacement to decrease to 4. (5 marks)
