I have two equations that are difficult to solve, so I am using fsolve to get the sol. But while running the program I encountered the error .Please help me or tell other way to solve these equations.

first equ;

 F1- (0.41*f1^2 + f1(1-f1))/(0.41*f1^2 + 2*f1(1-f1) +0.04*(1-f1)^2)=0

second equ;

0.589/(0.589 - 31.71/(104-51*F1)) - ((2826*4.479*E-7)*(176*62500*f1^2 + 2*62500*429.27*f1 - 2*62500*429.27*f1^2 + 2500*429.27 + 2500*429.27*f1^2 - 2*2500*429.27*f1))/(429.27*(1-f1) + 62500*f1) -1

;

program;;;;

function fcns  = eqs(z)
F1 = z(1);
f1 =z(2);
fcns(1) = F1- (0.41*f1^2 + f1(1-f1))/(0.41*f1^2 + 2*f1(1-f1) +0.04*(1-f1)^2);
fcns(2) = 0.589/(0.589 - 31.71/(104-51*F1)) - ((2826*4.479*E-7)*(176*62500*f1^2 + 2*62500*429.27*f1 - 2*62500*429.27*f1^2 + 2500*429.27 + 2500*429.27*f1^2 - 2*2500*429.27*f1))/(429.27*(1-f1) + 62500*f1) -1 ;
end

guess =[0.28 0.0244 ];
result = fsolve(@eqns,guess)

[Dhanvir Singh]

error;;

 fsol
Array indices must be positive integers or logical values.

Error in eqs (line 4)
fcns(1) = F1- (0.41*f1^2 + f1(1-f1))/(0.41*f1^2 + 2*f1(1-f1) +0.04*(1-f1)^2);

Error in fsolve (line 242)
            fuser = feval(funfcn{3},x,varargin{:});

Error in fsol (line 2)
result = fsolve(@eqs,guess)

Caused by:
    Failure in initial objective function evaluation. 
    FSOLVE cannot continue.

Answer 1

[madhan ravi]

guess = [0.28 0.0244];
result = fsolve(@eqs,guess)

function fcns  = eqs(z)
F1 = z(1);
f1 = z(2);
fcns(1) = F1- (0.41*f1^2 + f1*(1-f1))/(0.41*f1^2 + 2*f1*(1-f1) +0.04*(1-f1)^2);
fcns(2) = 0.589/(0.589 - 31.71/(104-51*F1)) - ((2826*4.479*1E-7)*(176*62500*f1^2 + 2*62500*429.27*f1 - 2*62500*429.27*f1^2 + 2500*429.27 + 2500*429.27*f1^2 - 2*2500*429.27*f1))/(429.27*(1-f1) + 62500*f1) -1 ;
end

[Dhanvir Singh]

Thank you sir!!

I have another inquiry .

Whatever guess I put ,it always return a same answer, i.e the exact answer then what's the use of guess.

[madhan ravi]

Not true, guess should in the proximity of the possible solutions.

Answer 2

[Alex Sha]

there are two solutions:

1:

F1: 0.458069398988435

f1: -1.13829069933547

2:

F1: 0.280093672719386

f1: 0.0244403974479464

[Walter Roberson]

Four solutions it turns out:

             f1                       F1
          1.25920378390736          1070015.92979626
       -0.0204942588521928         -68536267.4425476
        0.0244403974458328         0.280093672733541
         -1.13829070004027         0.458069399149128

[Alex Sha]

Take verification for those four solutions:

1: (1.25920378390736 1070015.92979626)

fev1=0.0239758458919823
fev2=-3.10862446895044E-15

2: (-0.0204942588521928 -68536267.4425476)

fev1=-19.8097575455904
fev2=3.5527136788005E-15

3: (0.0244403974458328 0.280093672733541)

fev1=-2.77555756156289E-16
fev2=-8.88178419700125E-16

4: (-1.13829070004027 0.458069399149128)

fev1=-1.11022302462516E-16
fev2=3.5527136788005E-15

the accuracy of the first two seems too lower

[Walter Roberson]

f1 is the four roots of

z^4 - (6077732260096151484325981836*z^3)/48676678745197603497996139375 - (2441998460292700770357164693701*z^2)/1703683756081916122429864878125 + (9739486432015774348021785204*z)/1703683756081916122429864878125 + 1223147048303704354962394632/1703683756081916122429864878125

F1 is related as

(340407827229812874745643267503*f1.^2)/2191837914062353460625 - (20253838448*f1.^3)/19 + (39001068488315423891730831977796*f1)/25571442330727457040625 - 955175915804501125862716674706/25571442330727457040625