code that I started:
# THIS IS NEEDED TO USE ARRAYS IN PYTHON:
from array import *
# THIS IS NEEDED TO MAKE PLOTS IN PYTHON:
import matplotlib.pyplot as plt
# IMPORT A ROUTINE FROM NUMPY USEFUL FOR CREATING AN
# ARRAY FILLED WITH ZEROS
from numpy import zeros
# THIS COMMAND CREATES AN ARRAY OF ZEROS WITH DESIRED SHAPE:
V=zeros([31,21])
newV=zeros([31,21])
# SET UP THE BOUNDARY VALUES: V=8 ON TOP OF BOX
iy=20
for ix in range(0,31):
V[ix,iy]=8.0
# DO THE ITERATIONS (MAY WANT TO ADJUST Nt)
Nt=100
for it in range(0,Nt):
for iy in range(1,20):
for ix in range(1,30):
.... I dont know how to finish ....
**** please help me complete the script please
I'm providing two solutions :-
#1
from visual import* from visual.graph import* import numpy as np x = y = 7 del = 2 vtop = [-1,-.67,-.33,.00,.33,.67,1] vbottom = [-1,-.67,-.33,.00,.33,.67,1] vleft = -1 vright = 1 vguess= 0 x,y = np.meshgrid(np.arange(0,lenx), np.arange(0,leny)) v = np.empty((x,y)) v.fill(vguess) v[(y-1):,:] = vtop v [:1,:] = vbottom v[:,(x-1):] = vright v[:,:1] = vleft boundary = 500 for iteration in range (0,boundary): for i in range(1,x): for j in range(1,y-1): v[i,j] =
v[i,j] = .25*(v[i+1][j] + v[i-1][j] + v[i][j+1] + v[i][j-1])
print (v)
#2
import matplotlib import matplotlib.pyplot as plt import numpy as np import time from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm plt.ion() fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.set_zlim(-1.01, 1.01) def draw_plot(x, y, u): ax.clear() ax.set_zlim(-1.01, 1.01) ax.plot_surface(x, y, u, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=0, antialiased=True) plt.pause(1e-5) # Create grid m = 21 mesh_range = np.arange(-1, 1, 2/(m-1)) x, y = np.meshgrid(mesh_range, mesh_range) # base case u = np.exp(-5 * (x**2 + y**2)) draw_plot(x, y, u) n = list(range(1, m-1)) + [m-2] e = n s = [0] + list(range(0, m-2)) w = s def pde_step(u): """ PDE calculation at a single time step t """ return (u[n, :]+u[:, e]+u[s, :]+u[:, w])/4. k = 5 U_step = u for it in range(500): U_step = pde_step(U_step) # Every k steps, draw the graphics if it % k == 0: draw_plot(x, y, U_step) while True: plt.pause(1e-5)
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