MaxStepSize

MaxStepSize
is an option to functions like NDSolve that specifies the maximum size of a single step used in generating a result.

Keep the largest step taken by NDSolve to be 0.01:

Out[1]=

Out[2]=

The default step control may miss a suddenly varying feature:

A smaller MaxStepSize setting ensures that NDSolve catches the feature:

Attempting to compute the number of positive integers less than

misses several events:

Setting a small enough MaxStepSize ensures that none of the events are missed:

For a length l, MaxStepFraction->f is equivalent to MaxStepSize