Mech 358 Lab 0 Solutions
Joshua Scurll
1
Problem 1
Part (a): V = 0.
Figure 1: Comparison of numerical and analytical solutions for V = 0.
Part (b): V = 1.
To four s.f. the value of the slope at y = 1 is u (1) = 2.500.
1
Figure 2: Comparison of numerical a
1. Consider the following problem: MW w W
+ u(ma Z lath?)
u(0,t) 2: u( ,t) 2 0
27m:
:3 ' _
u(m,0) 8111( L )
dened on 0 < 93 < L and t > 0.
Look for a soiution of the form u(a:, t) m butt) sin ('E
a. Separate variables and nd the differential e
Mech 358 Lab 0 Solutions
Joshua Scurll
1
Problem 1
The analytical solution for n = 1 is
u(t) = sin(t).
For the rst two gures, you were only required to plot u(t), not u (t).
For the energy plots, you were only asked to plot KE and PE for each n, but you s
Engineering Analysis
D. Coombs
MECH 358/MATH 358
Winter 2014
Assignment 4 Solutions
Problem 1.
Consider the Laplace equation problem (see class notes Feb 11):
2 2
+
=0
x2 y 2
x=0
= 0,
x=1
= f (y )
y = 0, 1 = 0
(1)
(2)
The general solution by Fourier si
Engineering Analysis
D. Coombs
MECH 358/MATH 358
Winter 2014
Homework 2
Due Feb 7, 2014
Note: You may want to refer to these solutions while working on Computer Lab 2.
Problem 1.
Basic nite dierence approximations
Three methods for estimating the rst deri
Mech 358 Lab 3 Solutions
1
Problem 1
The exact solution is
T (x) = x x4 .
Figure 1: Comparison of numerical, analytical and Fourier solutions.
1
2
Problem 2
Figure 2: Comparison of numerical and exact (Fourier series) solutions for dierent times.
You shou
Mech 358 Lab 2 Solutions
Joshua Scurll
1
Problem 1
Clearly, decreasing h at xed L improves the accuracy of the numerical solution. Roughly
1,000 grid points or more result in an absolute error of less than 103 across the domain.
Figure 1: Comparison of nu
Engineering Analysis
D. Coombs
MECH 358/MATH 358
Winter 2014
Assignment 3
Problem 1.
Consider the problem of steady state heat conduction in a rod with xed end temperatures, in
which there is a spatially-varying heat source applied to the rod. The BVP we