Runge-Kutta solvers for ordinary differential equations

rungekutta is a Python module that provides a framework for defining ordinary differential equations (ODEs) and solving these differential equations using Runge-Kutta methods.

Dependencies

• Python 3
• Numpy
• matplotlib for examples

Installation

The module can be installed via pip. If you want to develop this package, install the module in "editable" mode, i.e., add the -e flag to the install directive below

1. Clone the repository from GitHub and install it

git clone https://github.com/ajaust/python-runge-kutta
pip install --user python-runge-kutta

2. Install the module directly from GitHub

pip install --user https://github.com/ajaust/python-runge-kutta/archive/master.zip

The installed module is available under the name rungekutta.

Usage

This example shows how to to solve one of the provided ODE examples with an already implemented Runge-Kutta method. We use the explicit Euler method:

import matplotlib.pyplot as plt
import numpy as np
from rungekutta import rungekuttamethods as rk
from rungekutta import ordinarydifferentialequations as odes

# Start time
t0 = 0
# Time step size
dt = 2**-4
# End time
t_end = 4

# Initialize a simple ode y'(t) = y - 2*sin(t) as problem
ode = odes.SimpleODE()
# Initialize explicit Euler method as solver
ode_solver = rk.ExplicitEuler()
# Solve the ODE
y, time_arr, _ = rk.solve_ode(ode_solver, ode, t0, dt, t_end, verbose=False)
y = y.flatten()

# Plot solution using matplotlib
fig, ax = plt.subplots()
plt.title(f"Solution of a simple ODE")
ax.plot(time_arr, y, label=f"{ode_solver.get_name()}", marker="o")

# Plot the exact solution of the problem for comparison
x = np.linspace(t0, t_end)
ax.plot(x, ode.exact_solution(x), label="Exact solution")

ax.grid()
plt.xlabel("Time $t$")
plt.ylabel("Solution $y(t)$")

ax.set_xlim([t0 - 0.1, t_end + 0.1])
ax.set_ylim([-3.5, 2.0])

plt.legend()
plt.show()

For more examples check out the examples/ directory in the repository.