use of interp1 in ode solver: computational speed issues

Why when using matlab's function interp1 to get suitable values of a variable, x, in an ode solver (e.g. ode15s), causes a substantial decrease in computational time needed to get the final result of integrated values as the number of points in x increases? Is there a quick solution that avoids having a coarser representation (as compared to the integration time step) in order to increase computational speed?

Thank you,

Yiannis

[Ioannis Matthaiou]

Just to add to that, I think one of the main reasons is that fact that as the integration time step size decreases (as per the algorithm requirements) the variable x that is interpolated is assumed to have a constant value, which makes the integration faster (as it is easier to solve). I observed large integration times of x as having constant values.