initial commit of laplace

2d_laplace.py

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+##2D Laplace
+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib import cm
+from matplotlib.ticker import LinearLocator, FormatStrFormatter
+import matplotlib.pyplot as plt
+import numpy as np
+import os
+
+##variable declarations
+nx = 31
+ny = 31
+nt = 100
+c = 1
+dx = 2.0/(nx-1)
+dy = 2.0/(ny-1)
+sigma = .2
+dt = sigma*dx*dy
+
+
+##initial conditions
+p = np.zeros((ny,nx)) ##create a XxY vector of 0's
+pn = np.zeros((ny,nx)) ##create a XxY vector of 0's
+
+
+
+##plotting aids
+x = np.linspace(0,2,nx)
+y = np.linspace(0,2,ny)
+
+
+##time loop
+for n in nt:
+	pn[:] = p[:]
+	p[1:-1,1:-1] = (dy**2*(pn[2:,1:-1]+pn[0:-2,1:-1])+dx**2(pn[1:-1,2:]+pn[1:-1,0:-2]))/(2*(dx**2+dy**2)) 
+	p[0,0] = (dy**2*(pn[1,0]+pn[-1,0])+dx**2(pn[0,1]+pn[0,-1]))/(2*(dx**2+dy**2))
+	p[-1,-1] = (dy**2*(pn[0,-1]+pn[-2,-1])+dx**2(pn[-1,0]+pn[-1,-2]))/(2*(dx**2+dy**2)) 
+
+	p[:,0] = 0
+	p[:,-1] = y
+
+