Cork Institute of Technology
Bachelor of Engineering (Honours) in Structural Engineering-Stage 2
(NFQ – Level 8)
Autumn 2007
Numerical Methods and Computing II
(Time: 3 Hours)
Instructions Examiners: Dr. T. Creedon
Answer any four questions. Mr. P. Anthony
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).
(8 marks)
(c) Describe the Fixed-Point method for obtaining roots of an equation.
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. (9 marks)
Q2. (a) Describe Gaussian Elimination for solving a system of linear equations.
(9 marks)
(b) Outline the general structure of a program for solving systems of linear
equations using Gaussian Elimination. (8 marks)
(c) Describe the main pitfalls in using Gaussian Elimination and list some
techniques for improving the solution. (8 marks)
