Phyber NumInt

A numerical integrator for solving ODE systems

A simple package to solving ODE with different algorithms, written as explicitly as possible. I created this for a University course.

To use it you simply create an instance of the class ODEIntegrator

It takes the following parameters

• F that's the function that represents the ODE system (X' = F(X))
• X0 that's the initial conditions
• ti the initial time
• tf the final time
• dt the time step

The function F should be structured in the following fashion

def lorenz_system(t, X, sigma, beta, rho):
    '''
        x' = sigma(y - x)
        y' = x(rho - z) - y
        z' = x*y - beta*z
    '''
    x, y, z = X
    dxdt = sigma * (y - x)
    dydt = x * (rho - z) - y
    dzdt = x * y - beta * z
    return (dxdt, dydt, dzdt)

Then, the method solve of ODEIntegrator can be called with the method argument. The method argument is an enum member of IntegrationMethods. The following exist

• EULER_FORWARD
• EULER_BACKWARD
• EULER_IMPROVED
• EULER_IMPROVED
• RUNGE_KUTTA_2
• RUNGE_KUTTA_3
• RUNGE_KUTTA_4
• RUNGE_KUTTA_FEHLBERG_45

For example, ode_integrator.solve(IntegrationMethod.EULER_FORWARD)

One implementation would be

from phyber_numint import ODEIntegrator, IntegrationMethod
from phyber_numint.examples import lorenz_system

integ = ODEIntegrator(lorenz_system, (0., .5, .5), 0, 50, 1e-3, F_args=(8/3, 10, 25))
integ.solve(IntegrationMethod.RUNGE_KUTTA_4)
integ.show(True, plt_show=True)
integ.show((0,1), 'phase', plt_show=True, plt_kwargs={'s': 2})

Examples in the file examples.py

Also install matplotlib and tqdm to take advantage of every feature