Added Part E (Chris)

README.md

@@ -56,3 +56,22 @@ end
 ```
 
 ![nxn Interior Nodes, n = 10](./figures/figure2.png)
+
+### Part E
+
+```matlab
+[pw_se,w] = SE_diff(T,P,n);
+[root,fx,ea,iter] = bisect_final_project(@(T) SE_diff(T,0.001,25),.001,1,.1)
+```
+```matlab
+The same code was run five times, changing the value of n from 20 to 40 for intervals of 5.
+```
+
+| number of nodes | Tension (uN/um) | rel. error|
+| --- | --- | --- |
+|   3  |  0.0489  |  n/a    |
+|  20  |  0.0599  |  18.4%  |
+|  25  |  0.0601  |  0.30%  |
+|  30  |  0.0602  |  0.17%  |
+|  35  |  0.0603  |  0.16%  |
+|  40  |  0.0603  |  0.00%  |  

bisect_final_project.m~

@@ -0,0 +1,37 @@
+function [root,fx,ea,iter]=bisect_final_project(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:}); 

bisect_final_project_script.m

@@ -0,0 +1,2 @@
+[pw_se,w] = SE_diff(T,P,n);
+[root,fx,ea,iter] = bisect_final_project(@(T) SE_diff(T,0.001,40),.001,1,.1)