Transport equation with decay, a Python implementation. Full article can be found at http://www.firsttimeprogrammer.blogspot.com/2015/07/pdes-time-again-transport-equation.html

transportEq.py

#Transport equation with decay implementation

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

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

#Initial contitions
x0 = np.linspace(-2,15,10000)
t0 = 0

#Increment
dt = 0.01

#Wave speed k > 0
k = 3

#Decay constant b > 0
b = 2

#Scale
scale = 4

#Transport function
def u(x,t):
    return scale*np.exp(-(x-k*t)**2)*np.exp(-b*t)

t = []
g = []

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

k = 0
def animate(i):
    global k
    ax1.clear()
    plt.plot(x0,g[k],color='red',label='Time elapsed: '+str(round(t[k],4)))
    plt.grid(True)
    plt.ylim([-1,scale+1])
    plt.xlim([-2,15])
    plt.legend(loc=2)
    plt.title('Transport equation with decay')
    k += 1

anim = animation.FuncAnimation(fig,animate,frames=360,interval=20)
plt.show()