any method for system of first-order odes can be used to solve for tand tthe euler-cromer scheme an attractive choice from an implementationalaccuracyand efficiency point of view is the euler-cromer scheme where we take forward difference in ( and backward difference in ( ) nc tn un / unc un nc ( ( we can easily solve for the new unknowns nc and unc tn un / unc un tv nc nc ( ( remark on the ordering of the odes the ordering of the odes in the ode system is important for the extended model ( )-( imagine that we write the equation for first and then the one for the euler-cromer method would then first use forward difference for unc and then backward difference for nc the latter would lead to nonlinear algebraic equation for nc nc nc tnc unc if vis nonlinear function of this would require numerical method for nonlinear algebraic equations to find nc while updating nc through forward difference gives an equation for nc that is linear and trivial to solve by hand the file osc_ec_general py has function eulercromer that implements this methoddef eulercromer(fsfmtu_ v_ dt)from numpy import zeroslinspace n_t int(round( /dt)print 'n_t:'n_t linspace( n_t*dtn_t+ zeros(n_t+ zeros(n_t+ initial condition [ u_ [ v_