我当时在做一些数学作业，使用matplotlib进行可视化。然后我决定为它添加滑块（所有都是根据matplotlib demo完成的）。
这是最初的程序

import numpy as np

import matplotlib.pyplot as plt

a = 1

b = 1

start = 0

end = 1

tau_1 = 0.5

PRECISE_TIME = np.linspace(start, end + tau_1, 1000)

TIME_1 = np.arange(start, end + tau_1, tau_1)

u_0 = b

A_2_1 = []

A_3_1 = []

PRECISE_SOL = lambda t : b * np.exp(-a * t)

F = lambda t : 0

#A_2

def A_2(arr, const, times, tau):

    u_n = const

    for t in times:

        arr.append(u_n)

        u_n = (F(t) - a * u_n) * tau + u_n

    return np.array(arr)

#A_3

def A_3(arr, const, times, tau):

    u_n = const

    for t in times:

        arr.append(u_n)

        if len(arr) <= 1:

            u_n = (F(t) - a * const / 2 + const / tau) / (a / 2 + 1 / tau)

        else:

            u_n_1 = arr[-2] #u_(n-1)

            u_n = (F(t) - a*u_n) * 2 * tau + u_n_1 #U_(n+1)

    return np.array(arr)

plt.figure(figsize=(12, 40))

plt.plot(PRECISE_TIME, PRECISE_SOL(PRECISE_TIME), label='precise solution')

#plt.scatter(TIME_1, A_2_1, s=5, c='red', label='A_2 for step ' + str(tau_1))

#plt.scatter(TIME_1, A_3_1, s=8, c='green', label='A_3 for step ' + str(tau_1))

plt.plot(TIME_1, A_2([], b, TIME_1, tau_1), c='red', label='A_2 for step ' + str(tau_1))

plt.plot(TIME_1, A_3([], b, TIME_1, tau_1), c='green', label='A_3 for step ' + str(tau_1))

plt.legend()

plt.title("for a = " + str(a) + ", b = " + str(b) + ", f(t) = 0")

plt.show()

下面是带有滑块的一个（请注意，函数A_2和A_3与原始版本相同）：

import numpy as np

from time import sleep

import matplotlib.pyplot as plt

from matplotlib.widgets import Slider, Button

a = 1

b = 1

start = 0

end = 1

#A_2

def A_2(arr, const, times, tau, a):

    u_n = const

    for t in times:

        arr.append(u_n)

        u_n = (F(t) - a * u_n) * tau + u_n

    return np.array(arr)

#A_3

def A_3(arr, const, times, tau, a):

    u_n = const

    for t in times:

        arr.append(u_n)

        if len(arr) <= 1:

            u_n = (F(t) - a * const / 2 + const / tau) / (a / 2 + 1 / tau)

        else:

            u_n_1 = arr[-2] #u_(n-1)

            u_n = (F(t) - a*u_n) * 2 * tau + u_n_1 #U_(n+1)

    return np.array(arr)

#define initial parameters

init_tau = 0.1

#different times

PRECISE_TIME = np.linspace(start, end + init_tau, 1000)

TIME = np.arange(start, end + init_tau, init_tau)

#lambda expressions

PRECISE_SOL = lambda t : b * np.exp(-a * t)

F = lambda t : 0

# Create the figure and the line that we will manipulate

fig, ax = plt.subplots()

linep, = ax.plot(PRECISE_TIME, PRECISE_SOL(PRECISE_TIME))

lineA_2, = ax.plot(TIME, A_2([], b, TIME, init_tau, a), c='red')

lineA_3, = ax.plot(TIME, A_3([], b, TIME, init_tau, a), c='green')

#lineA_2 = ax.scatter(TIME, A_2([], b, TIME, init_tau), s=5, c='red', label="A_2")

#lineA_3 = ax.scatter(TIME, A_3([], b, TIME, init_tau), s=8, c='green', label="A_3")

ax.set_ylabel('Solution')

ax.set_xlabel('Time')

# adjust the main plot to make room for the sliders

fig.subplots_adjust(left=0.25, bottom=0.25)

# Make a horizontal slider to control the tau.

axtau = fig.add_axes([0.25, 0.1, 0.65, 0.03])

tau_slider = Slider(

    ax=axtau,

    label='Tau',

    valmin=0.01,

    valmax=0.5,

    valinit=init_tau,

)

# The function to be called anytime a slider's value changes

def update(val):

    lineA_2.set_ydata(A_2([], b, TIME, tau_slider.val, a))

    lineA_3.set_ydata(A_3([], b, TIME, tau_slider.val, a))

    #sleep(1)

    fig.canvas.draw_idle()

# register the update function with slider

tau_slider.on_changed(update)

# Create a `matplotlib.widgets.Button` to reset the sliders to initial values.

resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])

button = Button(resetax, 'Reset', hovercolor='0.975')

def reset(event):

    tau_slider.reset()

button.on_clicked(reset)

plt.show()

并且他们为相同的参数（τ）绘制了不同的图表
我认为我的计算机无法跟上重新计算结果的速度，所以我添加了time.sleep()函数，但这没有帮助