Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering
– Stage 2
(EMECH_8_Y2)
Autumn 2008
Computing and Numerical Methods
(Time: 3 Hours)
Instructions
Answer any FOUR questions.
All questions carry equal marks
Examiners: Dr. R. Sheehy
Mr. P. Clarke
Prof. M. Gilchrist
Q1. (a) Describe the Gauss Seidel Method for solving a system of linear equations.
Explain the use of relaxation methods to enhance convergence. (8 Marks)
(b) Write a program Gauss-Elim which uses the Gauss Elimination Method with partial
pivoting for solving a system of linear equations. (12 Marks)
(c) Illustrate using a suitable example an ill-conditioned system and list some techniques
for improving the solution. (5 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
() ()
()
()
1
xf
x f.xf
2
'
"
〈
is a necessary condition for
convergence of Newton Raphson method. (8 Marks)
(c) Write a program for locating single roots using any of the methods in part (a).
(7 Marks)
(d) Illustrate, using a suitable example an equation with multiple roots. Outline any
numerical method for obtaining multiple roots. (4 Marks)
