Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering – Stage 3
(Bachelor of Engineering in Mechanical Engineering – Stage 3)
Autumn 2005
Computing and Numerical Methods
(Time: 3 Hours)
Instructions
Answer any FOUR questions.
All questions carry equal marks.
Examiners: Dr. R. Sheehy
Prof. J. Monaghan
Mr. J. E. Hegarty
Q1. (a) Illustrate using suitable examples the concepts of (i) Stability (ii) Convergence as
applied to the numerical solution of ordinary differential equations. (6 Marks)
(b) Briefly describe (i) Single step (ii) Multi-step (iii) Predictor Corrector Methods and give
an example in each case. (9 Marks)
(c) Using any multi-step method obtain a numerical solution to the initial value problem
yyx
dx
dy −= 2 in the interval [0,1] with y(0) = 1 and h = .2 (5 Marks)
(d) Outline the structure of a program to implement the 4th order RK Method. (5 Marks)
Q2. (a) Illustrate using suitable examples both Initial Value and Boundary Value Problems. The
steady-state heat balance for a rod is 0)(
1
2
2
=−+ TTh
dx
Td
a. Obtain an analytical solution
for a 10m rod with h1 = .01 Ta = 20 , T(O) = 40 , T(10) = 200. (3 Marks)
(b) Use the Shooting Method to obtain a numerical solution to the problem in part (a).
(7 Marks)
(c) Use a Finite Difference Method with ∆X = 2 to solve the same problem as in part (a).
(7 Marks)
