1

SE_diff.m

@@ -1,91 +1,28 @@
-function [pw_se,w]=SE_diff(T,P,n)
-w = membrane_solution31(T,P,n);
-A = zeros(n,n);
-h = zeros(n,1);
-m = n+1; %Represents the number of nodes
-
-%Top Left Corner Interior Node
-for i = 2+m
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=1;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Top Right Corner Interior Node
-for i = m*2-1
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Bottom Left Corner Interior Node
-for i = m*m-(2*m)+1
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Bottom Right Corner Interior Node
-for i = (m*m)-m-1
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end 
-
-%The following represent the values for the interior nodes
-
-%Top Interior Row
-for i = 3+m:m*2-2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Bottom Interior Row
-for i = m*m-(2*m)+2:(m*m)-m-2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Left Interior Column
-for i = (2*m)+2,(2*m)+2:(m*m)-(2*m)+2
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=1;
-    A(i,i+m-1)=0; 
-    h(i) = 10;
-end
-%Right Interior Column
-for i = (3*m)-1,(2*m)+2:(m*m)-(2*m)+2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Inerior Nodes
-for i = (2*m)+3:(3*m)-2,(2*m)+3:(m*m)-(3*m)+3
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-
-
-dw_dx = (A(i,i)-A(i-1)+A(i,i+m)-A(i,i+m-1))/(2.*h);
-dw_dx'
-
-end 
+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
+    disp(m); % symmetric matrix 
 
+     h = 10/(n+1);
+    % Compute dw_dx
+    dx = zeros(n+2,n+1);
+    for i = 2:n+2
+        dx(:,i-1)= (m(:,i)-m(:,i-1))/h;
+    end
+    disp(dx)
+    dw_dx = zeros(n+1,n+1);
+    for i = 1:n+1
+        %dw_dx((i:n+1),i) = (dx(i,i)+dx(i+1,i))/2;
+        %dw_dx((i-1:n+1),i+1) = (dx(i,2)+dx(i+1,2))/2;
+        %dw_dx(i,3) = (dx(i,3)+dx(i+1,3))/2;
+        %dw_dx(i,4) = (dx(i,4)+dx(i+1,4))/2;
+        %i = i+1; 
+    end 
+    disp(dw_dx)
 
-
+    % Compute dw_dy