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I am trying to use poisson equation to plot the electric scalar potential in close 2D space. The details in in this video and this one

The following in written in Matlab for quick prototype.

    % solve matrix
    clearvars
    % number of rows ans columns
    m = 21
    n = 41
    
    % m = 3
    % n = 3
    % initialise arrays
    U = zeros(m*n,m*n);
    
    dx = 0.01;
    dy = 0.01;
    
    for i = 1:m
        for j = 1:n
            index = (i-1)*n+j;
            U(index, index) = -2/dx^2 -2/dy^2;
            if j-1 > 0
                U(index,index-1) = 1/dx^2;
            end
    
            if j+1 <= n 
                U(index,index+1) = 1/dx^2;
            end
    
            if i-1 > 0
                U(index,index-3) = 1/dy^2;
            end
    
            if i+1 <= m
                U(index,index+3) = 1/dy^2;
            end
        end
    end
    
    % U
    
    V0 = 0.5
    % U*results =B
    B = zeros(m*n,1);
    B((m-1)*n+1:m*n, 1) = -V0/dy^2;
    
    
    % Solve Linear Equations in Matrix Form
    results = linsolve(U,B);
    
    final =zeros(m,n);
    
    for k = 1:m
        final(k,:) = results((k-1)*n+1:k*n);
    end    
    
    % plot final results
    f1 = figure('Name','Voltage surface plot','NumberTitle','off');
    [X,Y] = meshgrid(0:0.1:4, 0:0.1:2);
    s = surf(X,Y,final,'FaceAlpha',0.5)
    title("Potential V(x,y) for finite conducting box, " + "V_0=" + V0 + " volts")

    f2 = figure('Name','imagesc','NumberTitle','off');
        
    clims = [4 18];
    imagesc(X(1,:), Y(:,1), final)
    title("Potential V(x,y) for finite conducting box, " + "V_0=" + V0 + " volts")

Image from the author.

enter image description here

Image from me.

enter image description here

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    $\begingroup$ How do your results differ from what is expected? What are you comparing your computed solution against to determine its accuracy? Please add more details to clarify your question $\endgroup$
    – whpowell96
    Commented Jul 2 at 23:56
  • $\begingroup$ @whpowell96 In my simulation for any location y<= 1.8 are 0 volts. But this is definitely incorrect from my intuition $\endgroup$
    – kile
    Commented Jul 2 at 23:59
  • 1
    $\begingroup$ It was incorrect to state in my initial commnet that there was a problem with the calculation method. Apologies. However, I still do not understand why your code contains "3" like index+3 or index-3. $\endgroup$
    – HEMMI
    Commented Jul 7 at 1:19
  • $\begingroup$ This post does not contain a question. What is it you are asking? $\endgroup$ Commented Jul 8 at 16:56

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