New algorithms for numerical integration and ODE solutions

[Namir]

Wes,

I try to use 16 instead of 4, but it seems I failed miserably in my updates. One function gave more error while another one cause run-tine overflow!

Last year an Australian calculator fan sent me improvements on my Romberg-Simpson method. He sent several versions, each slightly better than the one before it. He finally sent me two Excel files that included a good set of test functions. He even included a Timer routine that the VBA code used to measure the time for executing integration routines. I will soon be updating that document and post his Excel test files. You can look at his VBA code for the Romberg method. He performed special test to bring in early termination for the iterations when that was possible. The Excel test files allows you to show or hide the results. Pretty cool stuff.

Namir