fsolve message "Equation solved, inaccuracy possible"

Question

sina 2018-9-18

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https://ww2.mathworks.cn/matlabcentral/answers/419621-fsolve-message-equation-solved-inaccuracy-possible

评论： Alex Sha 2024-9-28，3:17

Hi

I want to solve a system of nonlinear equations using fsolve. But I get "Equation solved, inaccuracy possible." and all x are incorrect. By changing initial guess, nothing improves!

I appreciate your help

Regards,

Fun = @xisolver1;
x0 = [1e-4 1e-4 1e-4 1e-4 1e-4 1e-2 1e-2];
% options = optimoptions('fsolve','OptimalityTolerance',1e-20, 'FunctionTolerance', 1e-20);
options = optimoptions('fsolve','Display','iter','TolFun',1e-40,'TolX',1e-40);
xr = fsolve(Fun, x0, options);
function y = xisolver1(x)
T = 31.65 + 275.15;
lnK1 = 132.899 + (-13445.9/T) + -22.4773*(log10(T)/log10(exp(1)));
lnK2 = 216.05 + (-12431.7/T) + -35.4819*(log10(T)/log10(exp(1)));
lnK3 = 231.465 + (-12092.1/T) + -36.7816*(log10(T)/log10(exp(1)));
K1 = power(exp(1),lnK1);
K2 = power(exp(1),lnK2);
K3 = power(exp(1),lnK3);
KS1 = 1/K1;
KS2 = 1/K2;
KS3 = 1/K3;
% mole
n_CO2 = 6.3746;
n_K2CO3 = 9.7119;
n_H2O = 358.8905;
n_T = n_CO2 + n_K2CO3 + n_H2O;
% mass - gr/s
m_T = 8088.2946;
% molecular weight
MW_CO2 = 44.0095;
MW_CO3 = 60.0089;
MW_HCO3 = 61.0168;
MW_OH = 17.0073;
MW_H3O = 19.0232;
MW_H2O = 18.01528;
MW_K = 39.098;
MW_K2CO3 = 138.2055;
MW_KHCO3 = 100.1151;
% mole fraction
X_CO2T = (n_CO2 + n_K2CO3)/n_T;
X_K__ = 2*(n_K2CO3/n_T);
% mole number
N_CO2T = (n_CO2 + n_K2CO3);
y(1) = K1*(x(6)^2) - 1*x(4)*x(5);
y(2) = K2*x(3)*x(6) - 1*x(5)*x(2);
y(3) = K3*x(1)*(x(6)^2) - 1*x(5)*x(3);
y(4) = x(7) + x(5) - (2*x(2) + x(3) + x(4));
y(5) = x(1) + x(2) + x(3) - ...
    N_CO2T/(m_T/(x(1)*MW_CO2 + x(2)*MW_CO3 + x(3)*MW_HCO3 + x(4)*MW_OH + ...
    x(5)*MW_H3O + x(6)*MW_H2O + x(7)*MW_K));
y(6) = x(1) + x(2) + x(3) + x(4) + x(5) + x(6) + x(7) - 1;
y(7) = x(7) - (2*n_K2CO3)/(m_T/(x(1)*MW_CO2 + x(2)*MW_CO3 + x(3)*MW_HCO3 + x(4)*MW_OH + ...
    x(5)*MW_H3O + x(6)*MW_H2O + x(7)*MW_K));

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John D'Errico 2019-4-26

编辑：John D'Errico 2019-4-26

You should understand that

log10(T)/log10(exp(1))

is equivalent to the simple

log(T)

That is, log(T) is the NATURAL LOG of T?\

As well, why would you do this?

K1 = power(exp(1),lnK1);

You seem to understand that exp(1) yields the number e. So just use

K1 = exp(lnK1);

sina 2019-4-26

You're absolutly right, I modified that.

Do you have any idea about the question?

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Answer 1

Matt J 2018-9-18

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编辑：Matt J 2018-9-18

在 MATLAB Online 中打开

But the solution you got solves the equations quite well and also zeros the optimality measure quite well. If the wrong solution solves the equations, then the equations are to blame.

                                         Norm of      First-order   Trust-region
 Iteration  Func-count     f(x)          step         optimality    radius
        8        0.959589                             1               1
       16     2.73535e-08       0.901598       2.81e-06               1
       24     5.66403e-09      0.0230512       1.72e-06            2.25
       32     1.82444e-11     0.00549156       9.15e-08            2.25
       40     3.05915e-16    0.000351564       3.73e-10            2.25
       48     8.60818e-21    0.000134172       3.73e-13            2.25

4 个评论
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sina 2018-9-18

编辑：sina 2018-9-18

This worked better, However, because of K value I don't know maybe this is normal, and we can accept x

sina 2018-9-18

It worked however I got "Equation solved, inaccuracy possible." but I think for my case I can ignore the error!

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Answer 2

Alex Sha 2019-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/419621-fsolve-message-equation-solved-inaccuracy-possible#answer_371643

Multi-solutions:

1:

x1: 1.00788811123075E-6

x2: 0.0083586258586415

x3: 0.0330975342164431

x4: 0.000243072462467804

x5: 4.25824266670525E-13

x6: 0.908241901178143

x7: 0.0500578583957681

2:

x1: 0.0398069369652828

x2: 4.09226387610729E-13

x3: -6.59445321197498E-9

x4: -7.80181990889573E-15

x5: -0.0480652696493024

x6: 0.960193076222411

x7: 0.0480652630556597

3:

x1: -0.00867531212733977

x2: 3.28114366134408E-10

x3: 0.0504921742289807

x4: -1.14968645806141E-9

x5: -1.22255237713138E-9

x6: 0.907690964984408

x7: 0.0504921749580755

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sina 2019-4-26

Hi Alex Sha,

x should be positive. How did you solve it?

Alex Sha 2024-9-28，3:17

在 MATLAB Online 中打开

Positive solution:

x1: 2.69509999486066E-5
x2: 0.00844390016219942
x3: 0.0329852412877576
x4: 0.000183518150344329
x5: 5.65645880096964E-12
x6: 0.908303829637249
x7: 0.0500565597568442