membrane_solution.m

function [w] = membrane_solution(T,P,n)% Set up initial matrix
    % T = given tension (microNewton/micrometer)
    % P = given pressure (MPa)
    % n = number of interior nodes
    
    od = ones(n^2-1,1);
    od(n:n:end) = 0;
    k = -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);

    % Solve for unknown matrix, w
    y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector 
    w = k\y; %solves for w in micron

    [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)
end