fig illustration of the impact of resolution (time steps per periodand length of simulation righthoweverafter - periods the errors have grown (lower left)but can be sufficiently reduced by halving the time step (lower rightwith all the methods in odespy at handit is now easy to start exploring other methodssuch as backward differences instead of the forward differences used in the forward euler scheme exercise addresses that problem odespy contains quite sophisticated adaptive methods where the user is "guaranteedto get solution with prescribed accuracy there is no mathematical guaranteebut the error will for most cases not deviate significantly from the user' tolerance that reflects the accuracy very popular method of this type is the runge-kutta-fehlberg methodwhich runs th-order runge-kutta method and uses th-order runge-kutta method to estimate the error so that can be adjusted to keep the error below tolerance this method is also widely known as ode because that is the name of the function implementing the method in matlab we can easily test the runge-kutta-fehlberg method as soon as we know the corresponding odespy namewhich is rkfehlbergcompare(odespy_methods=[odespy eulercromerodespy rkfehlberg]omega= x_ = number_of_periods= time_intervals_per_period=