# CS 3200: Introduction to Scientific Computing Assignment 5 solved

\$40.00

## Description

5/5 - (1 vote)

1. Solve the coffee cup problem analytically for 5 minutes based upon Newton’s law of cooling:
ππππππ
ππππ = βππ(ππππ β πππ π )
πππ π  = 19β, ππππ = 84β, ππ = 0.025/π π π π π π π π π π π π
By making sure the supplied program runs using Matlab. Write the function Tsexact which is
the analytical solution for use in the supplied matlab code. Use the solution to the in class
2. Using the supplied program to solve the coffee cup problem using the Forward Euler
Method calculate and compare your results to the analytical answer given by the provided
function.
β’ Plot the results for all algorithms using several different values for the step size β (β =
30π π , 15π π , 10π π , 5π π , 1π π , 0.5π π , 0.25π π )
β’ Using these results estimate the order of the error after the first step and at the end of
the integration. Describe how the error changes with changes in β. Use a graph
3. Implement the ODE23 method described in the book Moler in the test program you have
been given . For the standard equation dy/dt = f(t,y) (note y here is Tc above) the method
is given by
β’ S1 = f(tn,yn)
β’ S2 = f(tn + h/2, yn+h/2 S1)
β’ S3 = f(tn + 3h/4, yn+3h/4 S2)
β’ tn+1 = tn + h
β’ yn+1 = yn + h/9 ( 2S1 + 3S2 + 4S3)
β’ S4 = f(tn+1, yn+1)
β’ Errorn+1 = h/72 ( -5S1 + 6S2 + 8S3 -9 S4)
4. Plot the results for this algorithms using several different values for the step size β (β =
30π π , 15π π , 10π π , 5π π , 1π π , 0.5π π , 0.25π π )
5. Using these results estimate the order of the error after the first step and at the end of the
integration. Compare the actual error on the first step with the predicted error on the first
step.
6. Change the value of r in the problem being solved to r = 0.6. Does the error estimator blow
up in the same way as the solution when the solution becomes unstable?
2

What to turn in
For these assignments, we expect both SOURCE CODES and a written REPORT be uploaded
as a zip or tarball file to Canvas.
β’ Source code for all programs that you write, thoroughly documented.
o Include a README file describing how to compile and run your code.
β’ Your report should be in PDF format and should stand on its own.
o It should describe the methods used.
o It should explain your results and contain figures.