Added Part F

README.md

@@ -68,6 +68,73 @@ end
 ![nxn Interior Nodes, n = 10](./figures/figure2.png)
 
 ### Part E
+``` matlab
+function [pw_se,w] = SE_diff(T,P,n)
+
+    % Call function from part c to obtain vector w
+    w = membrane_solution(T,P,n);
+    % Create All Nodes Matrix (Interior & Exterior)
+    m = zeros(n+2);
+    c = vec2mat(w,n); % Vector w rearranged to n x n matrix.
+    m(2:n+1,2:n+1) = c; % insert matrix c into middle of m matrix
+    % m = symmetric matrix
+
+    h = 10/(n+1); % h = delta_x = delta_y (micron)
+
+    % Compute w bar
+    w_bar = zeros(n+1,n+1);
+    for i = 1:n+1
+        for j = 1:n+1
+            w_bar(i,j) = (m(i,j)+m(i,j+1)+m(i+1,j)+m(i+1,j+1))/4;
+        end
+    end
+
+    % Left side of the equation
+    left_side = zeros(n+1,n+1);
+    for  i = 1:(n+1)^2
+        left_side(i) = P * h^2*w_bar(i);
+    end
+    L = sum(sum(left_side));
+
+    % Compute dw_dx
+    dx = zeros(n+2,n+1);
+    for i = 2:n+2
+        dx(:,i-1)= (m(:,i)-m(:,i-1))/(h);
+    end
+
+    dw_dx = zeros(n+1,n+1);
+    for i = 1:n+1 % rows
+        for j = 1:n+1 % columns
+        dw_dx(i,j) = (dx(i,j)+dx(i+1,j))/2;
+        end
+    end
+
+    % Compute dw_dy
+    dy = zeros(n+1,n+2);
+    for i = 2:n+2
+        dy(i-1,:)= (m(i-1,:)-m(i,:))/(h);
+    end
+
+    dw_dy = zeros(n+1,n+1);
+    for i = 1:n+1 % rows
+        for j = 1:n+1 % columns
+        dw_dy(i,j) = (dy(i,j)+dy(i,j+1))/2;
+        end
+    end
+
+    right_side = zeros(n+1,n+1);
+
+    for i = 1:(n+1)^2
+        right_side(i) = (0.25*(dw_dx(i))^4+0.25*(dw_dy(i))^4+0.5*(dw_dx(i)*dw_dy(i))^2);
+    end
+    R = sum(sum(right_side));
+    R = (1000*10^3*0.3*10^-3*h^2)/(2*(1-0.31^2))*R;
+
+    pw_se = R - L;
+end
+```
+
+### Part F
 
 ``` matlab
 [pw_se,w] = SE_diff(T,P,n);