MATH 308, Spring 2016
PROJECT
Implementation of Euler's Method in MATLAB
Due: Thursday 04 / 21 / 2016
THE AGGIE CODE OF HONOR
"An Aggie does not lie, cheat, or steal, or tolerate those who do."
INSTRUCTIONS: The idea of this project is to understand, implement, and apply the Euler's method to solve
numerically a rst order Initial Value Problem. To this end, rst of all the student:
1. Will describe in detail the Euler's method.
2. Implement this method in MATLAB using an m-le (a simple text le where you can place MATLAB commands),
explaining clearly every step and parameters introduced there.
3. (10 pts.) Use a simple example, let's say: y 0 = −2y; y(0) = 3, to see how the code is working.
then, the student will apply the Euler's method to the solution of the problem shown below. The idea here is to
compare the approximated solution given by Euler's method with the exact one .
4. (PROBLEM. Drainage of a Water Tank ) Suppose that a vertical cylindrical tank, of diameter D, cylindical exit
of radius d and sectional area A at the very bottom of the tank, it is lled with water up to a height h0 . Now,
using the Bernoullis' equation and the law of conservation of mass
"... The total volume of water leaving the tank during ∆t (∆Vexit ) = The total volume of water supplied by
the tank during ∆t (∆VT ank )..."
nd a rst order dierential equation for the draining of a water tank (h(t) = height of the water at time t).
Solve the IVP using the Euler's method and compare it with the exact solution ( take h(0) = 2 ).
5. Finally, the student will write ( not by hand ) a report with the results obtained for 1 to 4. Just remember that
this is an individual work.