Added integrators for solving IVPs.

[davidrpugh]

This is a placeholder PR for discussing where in quantecon these additional integrators/solvers for IVPs should live. The included integrators/solvers add functionality to the scipy.integrate.ode class and are predominately used for teaching purposes (as theses solvers are generally slower and less accurate that the solvers included in scipy.integrate.ode). Having said that, I have seen examples of where these simple integrators have been used in published research.

I have currently included them as a top level module in quantecon but this is probably not where they belong. Although they are related to the numerical integration routines in quantecon.quad, they are distinct enough that I am not sure that they belong in quantecon.quad.

One possibility might be to mimic the structure of scipy.integrate and make a quantecon.integrate submodule and then move quad, ivp, and integrators there.

[coveralls]

Coverage decreased (-14.86%) when pulling 093f5b5 on davidrpugh:add-integrators into a2c6bf4 on jstac:master.

[davidrpugh]

Yikes! Definitely need to write some tests!

[jstac]

@davidrpugh Actually we're shifting the focus of the library from education to high performance high quality code. So I'm not sure we want to include integrators that are already supplied in SciPy unless they have significantly better performance. (The routines in quad have helped us get big speed gains relative to the numerical routines in SciPy.) I think a better place for this code would be a notebook discussing ODE solvers.

[davidrpugh]

@jstac

I agree. I will add a couple of these simple fixed step size integrators to demonstrate the performance gains for using the more advanced variable step size integrators available in SciPy.