Solving a simple ODE

In this example we will show how to solve a simple ODE using the ODE solver in beat. While this is not the main purpose of the package it might be useful to solve the single cell models.

First we import the necessary packages

import numpy as np
from time import perf_counter
import matplotlib.pyplot as plt

import beat

def simple_ode_forward_euler(states, t, dt, parameters):
    v, s = states
    states[0] = v - s * dt
    states[1] = s + v * dt

num_points = 5
num_states = 2
states = np.zeros((num_states, num_points))
states[1, :] = np.linspace(0, 1, num_points)
dt = 0.01
t_bound = 20.0
t0 = 0.0

V_index = 0

nT = int((t_bound - t0) / dt) - 1
V = np.zeros((nT, num_points))
t0 = perf_counter()
beat.odesolver.solve(
    fun=simple_ode_forward_euler,
    t_bound=t_bound,
    states=states,
    V=V,
    V_index=V_index,
    dt=dt,
    parameters=None,
)

fig, ax = plt.subplots()
for i in range(num_points):
    ax.plot(V[:, i])
fig.savefig("simple.png")