Step size adjustment of ODE15s

Hello

I have problems to understand how the ODE15s (using NDFs) is adjusting the step size. I went through the documentation by LAWRENCE F. SHAMPINE "THE MATLAB ODE SUITE". However, I cannot find (or dont understand), if there is a rejection of old or new time step, or if there is a tolerance for a new time step ?

If there is any literature about varying time step in BDFs (or NDFs), I would be happy to receive suggestions. Else, if someone could explain me how ODE15s is changing the step size, I would be more than grateful for that.

Best wishes, Daniel Baeriswyl

Answer 1

[Siddharth Sundar]

I understand that you want to some information about how ode15s adjusts the time step size.

In general, in the absence of step failures, it does take account of tolerances and the order of accuracy of the formula being used. There appear to be some heuristics for dealing with failed steps and other difficulties. Usually the goal is to let the estimated error, the order of the formula, and the tolerance decide how to choose the next step size, but when problems occur, one is not always confident in the error estimate, and also one does not want the step size to increase or decrease too rapidly. Consequently, not all step size computations will end up using the estimated error and tolerances, but generally they do. The MATLAB source code for ode15s is shipped with the product, so you could try inserting a breakpoint and stepping through the code in order to see exactly what the function is doing.