In the MATLODE_Example_ERK_ADJ_Integrator script, if you change
Time_Interval = [0 20]
to, e.g.,
Time_Interval = [0 10 20]
an error is thrown. I think this is because of
OPTIONS.Quadrature = Quadrature;
in MATLODE_ERK_ADJ_Integrator in line 171 (and possibly others). There, the function handle is overwritten with the numeric integration value after the first for-loop execution. I am not sure how to fix this appropriately.