1

README.md

@@ -2,7 +2,7 @@
 
 ## Part A
 ### Problem Statement
-Create a function that uses the central finite difference approximation to solve for the displacements of a membrane with 3 x 3 interior nodes. The function should take the pressure and tension as inputs and output a column vector, w.
+Create a function called membrane_solution3 that uses the central finite difference approximation to solve for the displacements of a membrane with 3 x 3 interior nodes. The function should take the pressure (P) and tension (T) as inputs and output a column vector, w.
 
 ``` matlab
 function [w] = membrane_solution3(T,P) % Set up initial matrix
@@ -26,15 +26,18 @@ end
 
 ## Part B
 ### Problem Statement
-Using the function from part A as well as a given tension of 0.006 and a given pressure of 0.001, solve for w and plot the result in 3 dimensions
+Using the function from part A as well as a given tension of 0.006 uN/um and a given pressure of 0.001 MPa, solve for w and plot the result in 3 dimensions
 
 ``` matlab
 [w] = membrane_solution3(0.006,0.001);
 ```
 
 ![3x3 Interior Nodes](./figures/figure1.png)
 
-### Part C
+## Part C
+### Problem Statement
+Create a function called membrane_solution that uses the central finite difference approximation to solve for the displacements of a membrane with n x n interior nodes.  The function should take the pressure (P), tension (T), and number of interior nodes (n) as inputs and output the column vector, w.
+
 ```matlab
 function [w] = membrane_solution(T,P,n)% Set up initial matrix
     % T = given tension (microNewton/micrometer)
@@ -56,7 +59,8 @@ function [w] = membrane_solution(T,P,n)% Set up initial matrix
 end
 ```
 
-### Part D
+## Part D
+### Problem Statement
 ``` matlab
 [w] = membrane_solution(0.006,0.001,10)
 ```

SE_diff.m

@@ -8,21 +8,36 @@ function [pw_se,w] = SE_diff(T,P,n)
     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)
+    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
+
+        left_side(i) = P * h^2*w_bar(i);
+    end
+
     % 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 
-    
+disp(dw_dx)
     % Compute dw_dy
     dy = zeros(n+1,n+2);
     for i = 2:n+2
@@ -35,7 +50,7 @@ function [pw_se,w] = SE_diff(T,P,n)
         dw_dy(i,j) = (dy(i,j)+dy(i,j+1))/2;
         end 
     end 
-    
+   disp(dw_dy)
     pw_se = zeros(n+1,n+1);
 
     for i = 1:(n+1)^2