Метод Ойлера

import numpy as np
import matplotlib.pyplot as plt
 
def foo1(x, y, beta):
    return 1 + 0.4 * np.sin(x) - beta * y * y
 
 
def euler(f, x_0, y_0, a, b, beta, h=0.1):
    n = round((b - a) / h)
    y = y_0
    ys = [y_0]
    for i in range(0, n):
        y = y + h * f(round(x_0 + h*i, 1), y, beta)
        ys.append(y)
    return ys
 
 
a = 0
b = 1
h = 0.1
y_0 = 0
x_0 = 0
fig = plt.figure()
xs = np.arange(a, b+h, h)
plt.figure()
for n in range(0, 5):
    beta = 1+0.25*n
    syst = euler(foo1, x_0, y_0, a, b, beta, h)
    ys = syst[0]
    plt.plot(xs, ys, label='beta = ' + str(n))
    #print(i, syst)
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.title('third subtask')

def method_euler(h=0.1):
    global y
    print('Task 3')
    table = PrettyTable()
    table.field_names = ["x", "betan", "y"]
    fig, ax = plt.subplots(figsize=(12, 6))
    # Define parameters
    betan = np.array([1.0, 1.25, 1.5, 1.75, 2.0])
    for beta in betan:
        f = lambda x, y: 1 + 0.4 * np.sin(x) - beta * y * y  # ODE
        x = np.arange(0, 1, h)  # Numerical grid
        y0 = 0  # Initial Condition
 
        # Explicit Euler Method
        y = np.zeros(len(x))
        y[0] = y0
        for i in range(0, len(x) - 1):
            y[i + 1] = y[i] + h * f(x[i], y[i])
        plt.plot(x, y, marker='D', markersize=12)  # Approximate
        # plt.plot(x, -1 - 0.4 * np.sin(x) + beta * y)  # Exact
    print(y)
    plt.grid(which='both', linewidth=1.5, linestyle='-', color='gray')
    ax.tick_params(which='major', length=8, width=2)
    ax.tick_params(which='minor', length=8, width=2)
    ax.minorticks_on()
    ax.grid(which='major',
            linewidth=2)
    ax.grid(which='minor',
            linestyle=':')
    plt.title("'Approximate and Exact Solution for Simple ODE'")
    plt.xlabel("x")
    plt.ylabel("y")
    legend = plt.legend(betan, title='Legend',
                        loc='upper left', shadow=True, fontsize='x-large',
                        frameon=True, title_fontsize=15, framealpha=1)
    frame = legend.get_frame()
    frame.set_facecolor('black')
    frame.set_edgecolor('red')
    mplcyberpunk.add_glow_effects()
    mplcyberpunk.add_gradient_fill(alpha_gradientglow=0.5)
    plt.show()
    fig.savefig('Euler.png', dpi=300, bbox_inches='tight')
 
 
method_euler()

ys = euler(foo1, x_0, y_0, a, b, beta, h)