odecast

_images/odecast-logo.png

odecast is a Python library for solving ordinary differential equations of arbitrary order. Equations are written in their natural form, and odecast performs the reduction to a first-order system that numerical integrators require. Numerical solutions are computed with SciPy, closed-form solutions with SymPy.

from odecast import var, Eq, solve

# y'' + 0.3 y' + y = 0,  y(0) = 1,  y'(0) = 0
y = var("y")
eq = Eq(y.d(2) + 0.3*y.d() + y, 0)
sol = solve(eq, ivp={y: 1.0, y.d(): 0.0}, tspan=(0, 10))

sol.t        # time points
sol[y]       # y(t)
sol[y.d()]   # y'(t)

Main features:

  • the order of each variable is inferred from the equations;

  • coupled systems of mixed order;

  • nonlinear terms such as y**2 or sp.sin(y);

  • vector- and matrix-valued variables and matrix products;

  • parameters, with compiled systems reused across parameter values;

  • initial value problems with events and resets, and boundary value problems with unknown parameters;

  • differential-algebraic equations, including index reduction;

  • validation of initial and boundary conditions before solving;

  • numerical (SciPy) and symbolic (SymPy) backends;

  • sensitivities with respect to parameters;

  • equilibria, linearization, phase portraits, bifurcations, periodic orbits, and fitting parameters to data;

  • delay and stochastic differential equations;

  • partial differential equations with the method of lines.

Contents

Indices and tables