The wave equation: a Python implementation. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/07/the-wave-equation-2d-and-3d.html

waveEquation.py

import numpy as np
from numpy import pi
import matplotlib.pyplot as plt
import matplotlib.animation as animation

plt.style.use('dark_background')

fig = plt.figure()
fig.set_dpi(100)
ax1 = fig.add_subplot(1,1,1)

#Wave speed
c = 1

#x axis
x0 = np.linspace(-pi,pi,10000)

#Initial time
t0 = 0

#Time increment
dt = 0.05

#Wave equation solution
def u(x,t):
    return 0.5*(np.sin(x+c*t) + np.sin(x-c*t))

a = []

for i in range(500):
    value = u(x0,t0)
    t0 = t0 + dt
    a.append(value)

k = 0
def animate(i):
    global k
    x = a[k]
    k += 1
    ax1.clear()
    plt.plot(x0,x,color='cyan')
    plt.grid(True)
    plt.ylim([-2,2])
    plt.xlim([-pi,pi])
    
anim = animation.FuncAnimation(fig,animate,frames=360,interval=20)
plt.show()