% cemLaplace01.m

% Solution of Laplace's equation
clear
clf
tic

% INPUTS  ================================================================

% Number of XY grid points (integer)
     Nx = 5;
% Range for X and Y values  [minX maxX minY maxY minZ maxZ]
     XY = [0 5];
% Boundary potential
     V0 = 100;
% tolerance for ending iterations
    tol = 0.1;

% SETUP ==================================================================

    V = zeros(Nx,1);
    minX = XY(1);  maxX = XY(2);
    x = linspace(minX, maxX,Nx);
    hx = x(2) - x(1);
    V(1) = V0;  V(Nx) = 0;

% CALCULATIONS ===========================================================

% dSum difference in sum of squares  /  n  number of iterations
dSum = 10; n = 0;
while dSum > tol
    sum1 =  sum(sum(V.^2));

    for nx = 2: Nx-1
           V(nx) = 0.5*(V(nx+1) + V(nx-1));
    end
    sum2 =  sum(sum(V.^2));
    dSum = abs(sum2 - sum1);
    n = n+1;
end

% exact solution
VT = -(V0/maxX)*x + V0;

% electric field
E = -gradient(V,hx);

% GRAPHICS ===============================================================

figure(1)
    set(gcf,'units','normalized','position',[0.05 0.2 0.3 0.4]);
    subplot(2,1,1)
    plot(x,V,'b','lineWidth',2);
    hold on
    plot(x,VT,'r','lineWidth',2);
    %set(gca,'xLim',[minX, maxX]);
    %set(gca,'yLim',[minY, maxY]);
    xlabel('x  [ m ]'); ylabel('V  [ V ]');
    set(gca,'fontsize',14)

    subplot(2,1,2)
    plot(x,E,'b','lineWidth',2)
    set(gca,'yLim',[0, 25]);
    xlabel('x  [ m ]'); ylabel('E  [ V / m ]');
    set(gca,'fontsize',14)

 % =======================================================================
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