Quick example

To get started, import the ivps and bvps from diffeqzoo. You must also import the backend, because diffeqzoo needs to now whether to build the ODEs in numpy or in jax.

>>> from diffeqzoo import ivps, bvps, backend
>>> backend.select("numpy")

Here, we chose the numpy backend. We could have also used backend.select("jax"). Now with this backend, numpy-implementations are available via backend.numpy. (Under the hood, this imports and exposes either jax.numpy or numpy).

Use this backend to create ODE problems.

>>> f_lv, u0_lv, _, f_args_lv = ivps.lotka_volterra()
>>> x_lv = f_lv(u0_lv, *f_args_lv)
>>> print(x_lv)
[-10.  10.]

>>> f_rb, u0_rb, _, f_args_rb = ivps.rigid_body()
>>> x_rb = f_rb(u0_rb, *f_args_rb)
>>> print(x_rb)
[-0.     1.125 -0.   ]

>>> f_sir, u0_sir, _, f_args_sir = ivps.sir()
>>> x_sir = f_rb(u0_sir, *f_args_sir)
>>> print(backend.numpy.round(x_sir, 1))
[3.00000e-01 9.98000e+01 9.96004e+05]

While all IVP problem creators have a similar API, the ODE functions are not necessarily unified.

>>> import inspect
>>> f1, *_ = ivps.three_body_restricted()
>>>
>>> f2, *_ = ivps.sird()
>>>
>>> print(inspect.signature(f1))
(Y, dY, /, standardised_moon_mass)
>>>
>>> print(inspect.signature(f2))
(u, /, beta, gamma, eta, population_count)

Here, one IVP is a first-order problem with multiple parameters, the other one is a second-order problem with a single parameter. Second-order ODEs are taken seriously in the diffeqzoo, because the second-order form can be solved faster.