devi method of finding root

plz find the attachment and

help me in executing this program

[sixwwwwww]

There is not attachment here. Try to attach again

[unhappy]

plzz check it...now

[sixwwwwww]

I have few questions here:

• Why you defining symbols when you are not using them

syms a b
x = a + 1j * b

• What user can input in this line: (give some example input)

f = input('enter function in terms of x=');

[unhappy]

 actually iam new to this software. 
it should b like complex form like a+ij*b  i.e x^2+log(x)*1i

Answer 1

[sixwwwwww]

Dear Unhappy, here is the solution if I understood your problem correctly:

syms a_sym b_sym
x_sym = a_sym + 1j * b_sym;
a = 1;
b = 2;         
e = 2.71828;                
tol = 1e-5;                      
da = e + a;
db = e + b  ;                  
count = 0;                      
while (~(abs(da) < tol) && ~(abs(db) < tol))
    f = double(subs(x_sym, [a_sym b_sym], [a b]));
    realF = real(f);
    imagF = imag(f);
    da = (realF * realF + imagF * imagF) / abs(f^2);
    db = (realF * realF - imagF * imagF) / abs(f^2);
    a = a - da;      
    b = b - db;
    count = count + 1;          
    if (count > 400)
        fprintf('Error...! Solution not converging !!! \n');  % printing the error message
        break;
    end
end
if (count < 400)
    fprintf('The solution = '); 
    fprintf('\nNumber of iteration taken = %d\n',count);
end

[unhappy]

thanks for your solution ....but here i cant enter the i/p(i.e f)...and da = ((real(f)*real(diff(eval(f,1))))+(imag(f)*imag(diff(eval(f,1)))))/abs(eval(diff(f,1)^2));

    db= ((real(f)*imag(diff(eval(f,1))))-(imag(f)*real(diff(eval(f,1)))))/abs(diff(eval(f,1)^2)); 
its differentiation of f(x) with respective x...

[sixwwwwww]

what is i/p(i.e f)? Also

diff(eval(f,1)) you mean you want to differentiate f with respect to x?

[unhappy]

yup ...and this is the source where i got this method ..."Metal Waveguides for Multi-Axial Light Guiding at Nanometer Scales" and from page no 39 u can find this method...its a small topic

[sixwwwwww]

Here is the code:

syms f_sym x
f_sym = eval(input('Input function in terms of x:', 's'));
a = 1;
b = 2;         
e = 2.71828;                
tol = 1e-5;                      
da = e + a;
db = e + b;                  
count = 0;
x_val = input('Input initial value of x: ');
while (~(abs(da) < tol) && ~(abs(db) < tol))
    diffF_sym = diff(f_sym, 1);
    f = double(subs(f_sym, x, x_val));
    diffF = double(subs(diffF_sym, x, x_val));
    realF = real(f);
    realdiffF = real(diffF);
    imagF = imag(f);
    imagdiffF = imag(diffF);
    da = (realF * realdiffF + imagF * imagdiffF) / abs(diffF^2);
    db = (realF * imagdiffF - imagF * realdiffF) / abs(diffF^2);
    x_val = x_val - f / diffF;
    a = a - da;      
    b = b - db;
    count = count + 1;          
    if (count > 400)
        fprintf('Error...! Solution not converging !!! \n');
        break;
    end
end
if (count < 400)
    fprintf('The solution = '); 
    fprintf('\nNumber of iteration taken = %d\n',count);
end

I have tried it for input: x^2+log(x)*1j and it is working fine now. You can check once by yourself as well

[unhappy]

thanks sir/mam.it works..but my final destination is to find root of analytical soluitons..but here in this i can get only no of iteration it taken.. i cant see final root

[sixwwwwww]

What do you mean by final root? you mean final value of x?

[unhappy]

yes....it's like you heard about newton raphson method for root finding... this method is similar one for finding roots..but more advantageous than newton one..

[sixwwwwww]

So here is your final code:

syms f_sym x
f_sym = eval(input('Input function in terms of x: ', 's'));
a = 1;
b = 2;         
e = 2.71828;                
tol = 1e-5;                      
da = e + a;
db = e + b;                  
count = 0;
x_val = input('Input initial value of x: ');
while (~(abs(da) < tol) && ~(abs(db) < tol))
    diffF_sym = diff(f_sym, 1);
    f = double(subs(f_sym, x, x_val));
    diffF = double(subs(diffF_sym, x, x_val));
    realF = real(f);
    realdiffF = real(diffF);
    imagF = imag(f);
    imagdiffF = imag(diffF);
    da = (realF * realdiffF + imagF * imagdiffF) / abs(diffF^2);
    db = (realF * imagdiffF - imagF * realdiffF) / abs(diffF^2);
    final_x = x_val;
    x_val = x_val - f / diffF;
    a = a - da;      
    b = b - db;
    count = count + 1;          
    if (count > 400)
        fprintf('Error...! Solution not converging !!! \n');
        break;
    end
end
if (count < 400)
    fprintf('The solution = ');
    fprintf('\nNumber of iteration taken = %d\n',count);
    fprintf(strcat('The root is  ', num2str(final_x), '\n'));
end

If you like this answer then accept the answer to help others finding the solution if they have such problem as well. Good luck!

[unhappy]

thanks..u really helped a lot....how can i find u on net..may b in future i can contact u easily

[sixwwwwww]

I answer here with the same nick. You can post your questions here if I will have answer to that I will reply. Also accept this answer. Good luck!

[unhappy]

thankyou...:)

[sixwwwwww]

You are welcome

[unhappy]

hello mam/sir.. if u could help me finding code for multilayer method in paper"Confinement loss evaluation based on a multilayer division method in Bragg fibers" small topic i.e (2)..i would be thankful...hoping a posiive response from you

[sixwwwwww]

Can you tell what should be done because probably I will not be able to understand the physics. May be you can create your code roughly as before and post here as a new question then anybody who will know will help you

[unhappy]

i hope u downloaded the paper..basically it is elecromagnetics i.e EM wave equations...and here in this paper if u read carefully u might b come across hankel functions..which is higher order bessel functions...eqations 3,6,10,14 should b implemented..if equation 3 is implemented rest is eazy

[unhappy]

here EM wave should b initialized(1a,1b),equation 3 should b implemented,rest is simple like multiplication,inverse..etc..if u have time read upto equation 15...u can clearly understand this

[sixwwwwww]

I read it. It is very complicated. Can you tell me what are the inputs and what are the outputs so that I can give you some idea. Also see the following link for initial considerations of Hnakel transform: http://www.mathworks.com/help/matlab/ref/besselh.html

[unhappy]

ok..i knew its complicated...but once have a look in "theory of bragg fibers". you can get some idea....here outputs are Ai,bi,Ci,Di i.e in eq=14 in "multilayer method"