ME 581
Assignment 6
(Due: November 24, 2015)
1. Write each of the following ODEs as an equivalent first order system of ODEs
a. y'= t + y + y'
b. y'= ty + y'
c. What are the necessary initial conditions to solve the system in a. and b.
2. Write each of th
Homework 5 solution
Problem 1
5
Evaluate numerically: (5 x 2 3)dx using various methods
0
(a) Value of integral using midpoint rule: J 5 f (2.5) 171.25
[ f (0) f (5)]
327.5
2
[ f (0) 4 f (2.5) f (5)]
(c) Value of integral using Simpsons rule: J 5
223.33
ME 581 Optional Project
Due: November 30, 2015 at 8:00AM EST
This project is optional. If you turn in this project the grade of this project will be averaged to
your midterm score. The average will replace the score you obtained in the midterm exam. We
wi
ME581 Homework 6 Solution
Q1. (a) Let y1: y, y2: y'
y2
d y1
y y y t
dt 2 1 2
(b) Let y1: y, y2: y', y3 = y'
y1 y2
d
y2 y3
dt
y3 ty1 y3
(c) y(t0), y'(t0) needed for (a)
y(t0), y'(t0), y'(t0) needed for (a)
t0 is arbitrary.
Q2 (a) Let y1: y, y2:
ME 581 Homework 7 Solutions
1
Problem 1
a) Assume that it is separable.
u(x, t) = G(x)Y (t)
Y (t)
= G (x) =
Y (t)
G(x)
This results in two ODEs, Y (t) = Y (t) and G (x) = G(x), which can easily be solved.
Y (t) = C1 et and G(x) = C2 cos( x) + C3 sin( x)
Homework 4
ME 581
Due October 29
This homework does not require written code.
Lagrange interpolation
Problem 1: Let " = 3, ' = 0, ) = and + = .
(a) Determine formulas for the Lagrange polynomials +," , +,' ,
Homework 3 Solutions
ME 581
Problem 1.
The exact solution of the problem can be easily obtained for comparison from the standard
operation:
= 1
The resulting solution will be:
1.099090
0.084034
0.317577
x
0.579482
0.201681
0.503852
It can be
Name (last, first)
ME 581 FINAL
December 9, 8:00AM to 10:00AM
Open Book, Open Notes
Instructions:
Write your last and first name on every page
Problem 1 [25]. Solve the Lapalces equation with a second order accurate finite
difference method on the region
ME 581 Homework 2 Solutions
1 Hand Calculations
Problem 1
e = x x = [1 1]
T
r = Ax b = [0.02 0.02]T
 r 
 b 
Relative residual =
0.02
= 0.005
4
Condition number ( A) = A   A1 = 50 =

4
200
 A   A_1 
Relative error
 r 
=200 0.005 =1
 b 
 e
Homework 2
ME 581
Due September 24 2015
For all the problems you need to write/print your solutions and plots and return
them as a single hard copy (on campus students) or as a single pdf file using SVN
(only off campus students).
The cod
Homework 3
ME 581
Due October 8 2015
For all the problems you need to write/print your solutions and plots and return them
as a single hard copy (on campus students) or as a single pdf file using SVN (only
ME 581
Homework 5
(Due: Tuesday November 10, 2015)
Problems 6 and 7 are to be solved by a computer program that you have written, upload
the code using SVN
Problem 1
Evaluate
Z 5 numerically
2
(5x + 3)dx
0
(a) Midpoint rule
(b) Trapezoid rule
(c) Simpsons
ME 581
Assignment 7
(Due: December 3, 2015)
You will need to write a fourth order RungeKutta subroutine to solve problems 1,2 and 3. Upload
the code using SVN
1. Consider the initial value problem:
y'= 16.81y
y(0) = 1
y'(0) = 4.1
a. Derive the analytical
ME 581
Assignment 8
(Due: December 10, 2015)
Problem 1 in this homework is to be done by writing a computer program. Upload the
code using SVN.
1. Given the heat equation ut = uxx 0 x 1, t 0 , with initial condition
u(0, x) = sin(x) 0 x 1, and boundary co
Homework 3
ME 581
Due October 15 2015
For all the problems you need to write/print your solutions and plots and return them
as a single hard copy (on campus students) or as a single pdf file using SVN (only off
campus students).
The codes are submitted us
ME581 Homework 1
Due: September 10, 2015
Programming problems
Write a computer program (in C/ fortran or matlab or python) find a root using bisection. Upload your code using
SVN. The name of your code should be last_name_hw1bisection.c (or .f or py etc)