function [u,x,y] = Helmholtz(f,g,bx0,bxf,by0,byf,D,Mx,My,MinErr,MaxIter)
%解方程： u_xx + u_yy + g(x,y)u = f(x,y)
% 自變量取值區域 D = [x0,xf,y0,yf] = {(x,y) |x0 <= x <= xf, y0 <= y <= yf}
% 邊界條件
% u(x0,y) = bx0(y), u(xf,y) = bxf(y)
% u(x,y0) = by0(x), u(x,yf) = byf(x)
% x軸均分為Mx段
% y軸均分為My段 
% tol 誤差因子
% MaxIter: 最大迭代次數
%[u,x,y]:方程u(x，y)在(x,y)點的函數值
x0 = D(1); xf = D(2); y0 = D(3); yf = D(4);
dx = (xf - x0)/Mx; x = x0 + [0:Mx]*dx;%構造內點數組
dy = (yf - y0)/My; y = y0 + [0:My]'*dy;
Mx1 = Mx + 1; My1 = My + 1;
%邊界條件
for m = 1:My1
    u([1 Mx1],m)=[bx0(y(m)) bxf(y(m))]; %左右邊界
end
for n = 1:Mx1
    u(n,[1 My1]) = [by0(x(n)); byf(x(n))];%上下邊界
end 
%邊界平均值作迭代初值
sum_of_bv = sum(sum([u([1 Mx1],2:My) u(2:Mx,[1 My1])']));
u(2:Mx,2:My) = sum_of_bv/(2*(Mx + My - 2));
for i = 1:Mx
    for j = 1:My
         F(i,j) = f(x(i),y(j)); G(i,j) = g(x(i),y(j));
    end
end
dx2 = dx*dx; dy2 = dy*dy; dxy2 = 2*(dx2 + dy2);
rx = dx2/dxy2; ry = dy2/dxy2; rxy = rx*dy2;
for itr = 1:MaxIter
    for i = 2:Mx
        for j = 2:My
            u(i,j) = ry*(u(i+1,j)+u(i-1,j)) + rx*(u(i,j+1)+u(i,j-1))+ rxy*(G(i,j)*u(i,j)- F(i,j)); %迭代公式
        end
    end
    if itr > 1 & max(max(abs(u - u0))) < MinErr%循環結束條件
        break; 
    end
    u0 = u;
end
u=u';