#sde_solve ###a tiny library for numerically solving stochastic differential equations

##Installation

• Clone this repo
• enter the resulting directory
• sudo python setup.py install or python setup.py install --user if you don't have superuser privileges.

##Use The purpose of this library is to produce numerical solutions to differential equations of the form:

d_rho = det_f(t,rho) dt + stoc_f(t, rho) dW

using the order-1.5 strong solver for non-autonomous equations from Kloeden and Platen, page 379.

There's only one function in this repo, sde_platen_15:

sde_platen_15(rho_init, det_f, stoc_f, times, dWs, e_cb)

The input variables are:

• rho_init: an initial value. This can be any object that supports arithmetic methods in principle, but it must be accepted as input by det_f and stoc_f, see below.
• det_f: the deterministic contribution to the derivative. This is a function with signature det_f(t, rho)
• stoc_f: the stochastic contribution to the derivative. This is a function with signature stoc_f(t, rho).
• times: values of time (in arb. units) at which the solution is to be calculated. In principle, can be any type which supports __getitem__. In practice, NumPy arrays work best. Note: As of the current version, sde_platen_15 assumes this iterable to have a fixed difference.
• dWs: iterable of values for the Wiener increment. This is not generated within the function, since it is often convenient for this variable to be in scope where sde_platen_15 is called.
• e_cb: Callback function with signature e_cb(t, rho, dW). This brings the interim values of time, solution and Wiener increment into whatever namespace in which e_cb is def'd.

##Example Coming soon

##Future Work

• Adaptive timesteps
• Switching the whole thing over to Julia, so I can decide at runtime whether to use an implicit method.