MATLAB: How to solve singularity problem while using fsolve

fsolvenonlinear

Hi,I am trying to solve for x in a equation using fsolve. Below is the code and equation:
a = 0.1886;
b = 0.6886;
c = 1.1886;
m = 0.31372;
x0 = 0.1;
F = @(x)[(((x-a)/(x-c))^(m))+((x-a)/(x-b))];
options = optimset('Display','iter','MaxFunEvals',1e20,'TolFun',2e-50,'TolX',2e-50);
[xd, fval, exitflag, output]= fsolve(F, x0, options)
However, I am getting 'No solution found' with a message: fsolve stopped because the problem appears to be locally singular. I have tried changing the options parameters and initial guess still getting same output. Any help is appreciated.
Thanks, KB

Best Answer

Try splitting the fsolve approach with real() and imag() because with real() i get something:
..
F = @(x)[real(((x-a)/(x-c))^(m))+((x-a)/(x-b))];
..
[xd, fval, exitflag, output]= fsolve(F, x0, options)
                                           Norm of      First-order   Trust-region
   Iteration  Func-count     f(x)          step         optimality    radius
       0          2        0.366931                          1.77               1
       1          4     0.000271336       0.207172         0.0421               1
       2          6     2.03148e-07     0.00645204        0.00109               1
       3          8     1.38596e-13    0.000186725       8.97e-07               1
       4         10     7.81816e-26    1.54486e-07       6.74e-13               1
       5         12     3.08149e-33    1.16029e-13       1.34e-16               1
Equation solved, inaccuracy possible.
The vector of function values is near zero, as measured by the selected value
of the function tolerance. However, the last step was ineffective.
<stopping criteria details>
xd =
          0.30
fval =
         -0.00
exitflag =
          3.00
output = 
       iterations: 5.00
        funcCount: 12.00
        algorithm: 'trust-region-dogleg'
    firstorderopt: 0.00
          message: 'Equation solved, inaccuracy possible.…'
repeat for the imag() part.
Or alternatively use abs() and arg()
all together, you should catch at least 2 poles on b and c.
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please click on the thumbs-up vote link,
thanks in advance
John
jgb2012@sky.com
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