I am new in MATLAB and trying to write this code on NEWTON-RAPHSON. Please help me to rectify the error in this code. I have shared the program with the error signal below. Its urgent. Any help will be highly appreciated.

syms x

f= cos(3*x) - x

x(1)=input('Enter your guess:');

tol=input('Enter the tolerance:');

fdash=diff((f));

for i=1:100

   sym x(i+1)=x(i)-(f(x(i))/fdash(x(i)));

   if abs((x(i+1)-x(i)))<tol;

        break

    end

end

root=x(i).

The error I get is:

??? Error using ==> mupadmex Error in MuPAD command: Index exceeds matrix dimensions.

Error in ==> sym.sym>sym.subsref at 1366 B = mupadmex('mllib::subsref',A.s,inds{:});

Error in ==> newtonraphson2 at 8 if abs((x(i+1)-x(i)))<tol;_ * * *

Answer 1

[Geoff Hayes]

Why do you have a sym at the line

 sym x(i+1)=x(i)-(f(x(i))/fdash(x(i)));

Shouldn't this just be an evaluation of the statement

 x(i+1)=x(i)-(f(x(i))/fdash(x(i)));

instead?

The error message is telling you that there is a problem at the line

 abs((x(i+1)-x(i)))<tol

As i, on the first iteration, is 1, then x(i) should be valid. Since the error message is index exceeds matrix dimension then that suggests that x(2) or x(i+1) is the problem.

EDIT

I don't have the Symbolic Toolbox so re-wrote the code as

 f = @(x)cos(3*x) - x;

 x(1) = input('Enter your guess:')
 tol  = input('Enter the tolerance:');

 fdash=@(x)3*(-sin(3*x)) - 1;

 for k=1:100
   x(k+1)=x(k)-(f(x(k))/fdash(x(k)));
   if abs((x(k+1)-x(k)))<tol;
        break
    end
 end

[Tuhin]

Thank you Geoff for replying. Now it is working. It was a great help for me.. Thanks again.

[Geoff Hayes]

Glad to have been able to help, Tuhin!