devi method of finding root

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unhappy 2013-10-14

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编辑： unhappy 2013-12-6

采纳的回答： sixwwwwww

plz find the attachment and

help me in executing this program

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sixwwwwww 2013-10-14

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编辑：sixwwwwww 2013-10-14

在 MATLAB Online 中打开

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

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sixwwwwww 2013-10-14

编辑：sixwwwwww 2013-10-14

在 MATLAB Online 中打开

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

sixwwwwww 2013-10-14

在 MATLAB Online 中打开

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!

sixwwwwww 2013-10-15

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 2013-10-15

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"

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