How to integrate ordinary differential equations with pulse-like time-varying parameters?

Problem.

I am simulating an ordinary differential equation with time-varying parameters as follows

p   = @(t) p0*( (T0 < t) & (t < T1) )
sol = ode15s(@(t,x) myode(t,x,p(t)),[t0 tf],x0)

where p(t) is a pulse of amplitude p0 and duration (T1-T0) (if T0 < T1).

Because of its adaptive time-step, the integrator "misses the pulse" if the time-step becomes larger that the pulse duration.

Naive solution.

A naive solution would be to constrain the MaxStep to (T1-T0)/2 to be sure that the pulse is detected by the integrator. However, this constrains the MaxStep at time where it is not really needed.

More efficient solution?

I am wondering if there is a more efficient way to do ensure that the pulse is detected.

[Star Strider]

Not really enough information so just guessing here, but have you considered if an event structure would allow you to do what you want? Checking to see if a derivative triggers a zero-crossing might work.

[Pierre S.]

Hi Star Strider. Thank you for answering. What would you need as extra information? My goal is to enforce the evaluation of the ode function at T0 + (T1-T0)/2 to be sure that the adaptive mesh do not miss the parameter "pulse". -Pierre

[Star Strider]

Posting (or attaching — use the ‘paperclip’ icon) the code for myode would do for a start, as well as information on p0, T0, and T1. We really cannot suggest a solution to a problem we cannot experiment with ourselves.

[RahulTandon]

pleas send the formulae for the two equations 1) The mymode function 2) The pulse train Awaiting an early reply!