Answer 1

A problem to integrate and the corresponding jacobian

>>> from scipy.integrate import ode
>>>
>>> y0, t0 = [ 1.0j , 2.0 ], 0
>>>
>>> def f (t, y, arg1):
>>> return [ 1j * arg1 * y[ 0 ] + y[ 1 ], - arg1 * y[ 1 ] ** 2 ]
>>> def jac(t, y, arg1):
>>> return [[ 1j * arg1, 1 ], [ 0 , -arg1 * 2 * y[ 1 ]]]

The integration
>>> r = ode(f, jac) . set_integrator
( 'zvode' , method = 'bdf' ,
with_jacobian = True )
>>> r . set_initial_value(y0,
t0) . set_f_params
( 2.0 ) . set_jac_params( 2.0 )
>>> t1 = 10
>>> dt = 1
>>> while r . successful() and r . t <
t1:
>>> r . integrate(r . t + dt)
>>> print ( " %g %g " % (r . t, r . y))

Hope this helps