Homework assigned 10/20, due 10/23
Adaptive Simpson's Rule
Choose a function that you know how to integrate. Put that
function in f.m and its antiderivative in f_int.m Choose an interval
of integration. Now use the adaptive Simpson's method *.m file to
integrate this function for a sequence of tolerances. Give me a table
that for each tolerance lists the tolerance, the number of nodes used,
the computed area, and then the error between the computed area and
the true area.
Choose a function for which an adaptive integration method will
be better than a standard uniform-mesh integration method. Explain
why an adaptive method will be better. Choose an interval of
integration. Again, use the adaptive Simpson's method *.m file to
integrate this function for a sequence of tolerances. Give me a table
that for each tolerance lists the tolerance, the number of nodes used,
and the computed area.
Adaptive Trapezoidal Rule
Modify the adaptive Simpson's method *.m program to be an
adaptive trapezoidal method.
Repeat the first adaptive Simpson's method problem, to test that
your program is working. Use the same f.m and f_int.m. Compare the
two methods. What's the difference and why did you expect this
difference?
Repeat the second adaptive Simpson's method problem.
Homework Amnesty
Hand in any late homework problems from the past six weeks.