## Ordinary differential equations

As with integration, SciPy has some extremely accurate general-purpose solvers for systems of ordinary differential equations of first order:

For real-valued functions, we have basically two flavors: `ode`

(with options passed with the `set_integrator`

method) and `odeint`

(simpler interface). The syntax of `ode`

is as follows:

ode(f,jac=None)

The first parameter, `f`

, is the function to be integrated, and the second parameter, `jac`

, refers to the matrix of partial derivatives with respect to the dependent variables (the Jacobian). This creates an `ode`

object, with different methods to indicate the algorithm to solve the system (`set_integrator`

), the initial conditions (`set_initial_value`

), and different parameters to be sent to the function or its Jacobian.

The options for integration algorithm are `'vode'`

for real-valued variable coefficient ODE solver, with fixed-leading-coefficient implementation (it provides Adam's method for non-stiff problems and BDF for stiff); `'zvode...`