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.