Intersection of two functions

Hi, I've been trying to solve a problem using the newton-raphson method for the intersection of two functions. I have a matlab code to find the roots of simpler functions which I have been trying to adapt to the problem. this is my code:

function root = newton(x,f,df,imax,tol)
% Input: x initial guess at the root
% f function to be evaluated
% df derivative of f with respect to x
% imax iteration maximum
% tol convergence criterion
% Output: root position of the root

%intialise parameters
    xold=x;
    fold=feval(f,xold); 

count=0;
for i=0:imax
    count=count+1;
    fold=feval(f,xold);
    dfold=feval(df,xold);

% Newton's algorithm
xnew = xold -(fold/dfold);

% CHECK: verify that derivative is not zero.

   while norm(fold)<tol  
  if df == 0
  error('Problem 0 gradient')
  end

% calculate equation 4
% CHECK: Excessive iterations
% test for convergence
if norm(fold)<tol
   root=xnew;
    return 
end
 end
xold=xnew;
end
error('max iterations reached')

end

I've been running this code where function f is

function z=trial(x)
z=(100.*exp(-x))-(5.*(sin((pi/2).*x)));
end

and function df is

function w=trial2(x)
w=(-100.*exp(-x))-((5/2).*cos((pi/2).*x));
end

My code is running however its reaching my max number of iterations and I'm not sure how to resolve this problem.

Thanks in advance

Answer 1

[James Tursa]

You missed the pi constant when taking the derivative of sin((pi/2).*x). You only pulled out the 1/2 constant instead of the entire (pi/2) constant. Try

w=(-100.*exp(-x))-(pi*(5/2).*cos((pi/2).*x));

Answer 2

[GG]

Ah, that actually plots it now. Thank you!