membrane_solution.m

function [w] = membrane_solution(T,P,n)
   
    od = ones(n^2-1,1);
    od(n:n:end) = 0;
    a = -4*diag(ones(n^2,1))+diag(ones((n^2)-n,1),n)+diag(ones((n^2)-n,1),-n)+diag(od,1)+diag(od,-1);

    y = -(10/(n+1))^2*(P/T)*ones(n^2,1);
    w = a\y;
grid on
    [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
    z = zeros(size(x));
    z(2:end-1,2:end-1) = reshape(w,[n n]);
    surf(x,y,z)
    title('Membrane Displacement')
    xlabel('X (\muM)')
    ylabel('Y (\muM)')
    zlabel('Displacement (\muM)')
    colormap jet
    shading interp
    disp(w)
end