Cork Institute of Technology
Bachelor of Engineering (Honours) in Structural Engineering - Stage 2
(NFQ Level 8)
Autumn 2006
Numerical Methods and Computing II
(Time: 3 Hours)
Instructions Examiners: Dr. T. Creedon
Answer any four questions. Mr. T. Corcoran
All questions carry equal marks. Prof. P. O’Donoghue
Q1. (a) Describe any two of the following methods for obtaining roots of an equation:
(i) Bisection
(ii) False-Position
(iii)Newton (8 marks)
(b) Write a Fortran program for locating single roots using one of the methods in
part (a). (7 marks)
(c) Show that if g and '
g
are continuous in an interval about the root and '
|()|1gx< for all
x in this interval and 0
x
is chosen in this interval, then the Fixed-Point method will
converge to the root. (7 marks)
(d) Illustrate using a suitable example an equation with multiple roots. Describe the
modified Newton’s method for obtaining multiple roots. (3 marks)
Q2. (a) Describe the Gauss Seidel method for solving a system of linear equations. (9 marks)
(b) Outline the general structure of a program for solving systems of linear equations
using the Gauss Seidel method. (8 marks)
(c) Describe the use of over-relaxation to improve the rate of convergence of the Gauss
Seidel method. (8 marks)
