Diferenciální rovnice pro začátečníky

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy.integrate import solve_ivp

pocatecni_podminka = [0.1]
meze = [0,10]

def rovnice(t, x, h=0):
    r = 1
    K = 1
    return r*x*(1-x/K) - h

t=np.linspace(*meze, 100)  # graf reseni
reseni = solve_ivp(
                   rovnice,
                   meze,
                   pocatecni_podminka,
                   t_eval=t, ## zde je možné zadat pole hodnot, kde se mají určit řešení
                   )
reseni

  message: The solver successfully reached the end of the integration interval.
  success: True
   status: 0
        t: [ 0.000e+00  1.010e-01 ...  9.899e+00  1.000e+01]
        y: [[ 1.000e-01  1.095e-01 ...  9.995e-01  9.995e-01]]
      sol: None
 t_events: None
 y_events: None
     nfev: 62
     njev: 0
      nlu: 0

fig,ax = plt.subplots(1)
ax.plot(t,reseni.y.T)

[<matplotlib.lines.Line2D at 0x7f9e9598fbc0>]

ax.set(
    ylim = (0,None),
    title = "Řešení diferenciální rovnice",
    xlabel=r"$t$",
    ylabel=r"$x$",
)
fig

df = pd.DataFrame(reseni.y.T, index=t)
df

	0
0.00000	0.100000
0.10101	0.109465
0.20202	0.119702
0.30303	0.130753
0.40404	0.142664
...	...
9.59596	0.999297
9.69697	0.999345
9.79798	0.999398
9.89899	0.999455
10.00000	0.999507

100 rows × 1 columns