משוואת לפלס על רשת

function solve(A,b) {
  const M=A.map((row,i)=>[...row,b[i]]), n=A.length;
  for(let c=0;c<n;c++) { let p=c; for(let r=c+1;r<n;r++) if(Math.abs(M[r][c])>Math.abs(M[p][c])) p=r;
    [M[c],M[p]]=[M[p],M[c]]; const d=M[c][c]; for(let j=c;j<=n;j++) M[c][j]/=d;
    for(let r=0;r<n;r++) if(r!==c) { const f=M[r][c]; for(let j=c;j<=n;j++) M[r][j]-=f*M[c][j]; } }
  return M.map(row=>row[n]);
}

function laplaceGrid(n,top) {
  const count=n*n, K=Array.from({length:count},()=>Array(count).fill(0)), b=Array(count).fill(0);
  const index=(r,c)=>r*n+c;
  for(let r=0;r<n;r++) for(let c=0;c<n;c++) { const k=index(r,c); K[k][k]=4;
    for(const [dr,dc] of [[-1,0],[1,0],[0,-1],[0,1]]) { const rr=r+dr,cc=c+dc;
      if(rr>=0&&rr<n&&cc>=0&&cc<n) K[k][index(rr,cc)]=-1; else if(rr<0) b[k]+=top; } }
  return solve(K,b);
}

console.log(laplaceGrid(2,4));

def solve(A,b):
    M=[row[:] + [b[i]] for i,row in enumerate(A)]
    n=len(A)
    for c in range(n):
        p=max(range(c,n),key=lambda r:abs(M[r][c]))
        M[c],M[p]=M[p],M[c]
        d=M[c][c]; M[c]=[value/d for value in M[c]]
        for r in range(n):
            if r!=c:
                f=M[r][c]; M[r]=[M[r][j]-f*M[c][j] for j in range(n+1)]
    return [row[n] for row in M]

def laplace_grid(n,top):
    count=n*n
    K=[[0]*count for _ in range(count)]
    b=[0]*count
    index=lambda r,c:r*n+c
    for r in range(n):
        for c in range(n):
            k=index(r,c); K[k][k]=4
            for dr,dc in [(-1,0),(1,0),(0,-1),(0,1)]:
                rr,cc=r+dr,c+dc
                if 0<=rr<n and 0<=cc<n: K[k][index(rr,cc)]=-1
                elif rr<0: b[k]+=top
    return solve(K,b)

print(laplace_grid(2,4))