setting Boundary condition X^2-Y^2 for solving Laplace equation for NxN grid.

[User 13593623]

i am trying to write a code to solve Laplace equation using Successive

Over relaxation(SOR)on a NXN matrix boundary condition is X^2-y^2 i dont know how to set this boundary condition on the Mesh created by me here is the code

import numpy as np
from pylab import *
import sys
import copy
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
L =[[]for i in range(2)]
N=int(input("Enter a number N for N x N grid: "))
h=1/N
def clear_list1():
L[1].clear()
L[0].clear()
iterat=0
error=0.75
clear_list1()
xx=np.arange(0,N,h)
yy=np.arange(0,N,h)
x,y = np.meshgrid(xx,yy)
phi= copy.deepcopy((x**2-y**2))
phi[1:-1,1:-1]=0
phi_new = copy.deepcopy(phi)
resid=np.zeros((N,N))

while True:
if iterat<21:

   for w in np.linspace(1,2,11):
       for i in range(1,N-1):
           for j in range(1,N-1):
               phi1=(phi\[i+1,j\]+phi\[i-1,j\]+phi\[i,j+1\]+phi\[i,j-1\])/4
               phi\[i,j\]=w\*phi1+(1-w)\*phi1
               
   Sumresidual=0
   for i in range(1,N-1):
       for j in range(1,N-1):
           resid\[i,j\]= -4\*phi\[i,j\]+phi\[i+1,j\]+phi\[i-1,j\]+phi\[i,j+1\]+phi\[i,j-1\]
           Sumresidual=Sumresidual+(resid\[i,j\])\*\*2
else:
    break
iterat=iterat+1
p=np.sqrt(Sumresidual)
L\[0\].append(p)
L\[1\].append(w)

ax = plt.axes()
ax.xaxis.set_major_locator(ticker.MaxNLocator(5))

plt.plot(L[0],L[1])
plt.yscale('log')
plt.xlabel('w')
plt.ylabel('|| residual ||')
plt.title('effect of w on residual')
plt.show()

[Victor Nijegorodov]

And what does your code have to do with the C / C++ / MFC Forum?