Three nonlinear equation with initial guess

Question

Nihal Yilmaz 2022-6-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734530-three-nonlinear-equation-with-initial-guess

评论： MOSLI KARIM 2022-8-12

How can I solve this question? Please help me, Thank you.

equations are

-0.06*(x^2)-1.06*(z^2)+3.18*x+3.18*z+1.59*y-2.06*x*y-3.12*x*z-2.385-1.06*y*z=0

2.63*(x^2)-1.63*(y^2)-2.63*(z^2)-3.945*x+3.945*y+3.945*z-4.76*y*z=0

z-7.5*y+5x*y+5*y*z=0

initial guess x=y=z=0

x=?

y=?

z=?

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MOSLI KARIM 2022-8-12

在 MATLAB Online 中打开

function bvp_prb14
tspan=[0; 15];
y0=[0;0;0];
[t,x]=ode45(@fct,tspan,y0)
X=x(:,1)  %%%  x solution 
Y=x(:,2)  %%% YOUR Y
Z=x(:,3) %%%YOUR Z 
table(X,Y,Z)
function yp=fct(t,x)
yp=[-0.06*(x(1)^2)-1.06*(x(3)^2)+3.18*x(1)+3.18*x(3)+1.59*x(2)-2.06*x(1)*x(2)-3.12*x(1)*x(3)-2.385-1.06*x(2)*x(3);
2.63*(x(1)^2)-1.63*(x(2)^2)-2.63*(x(3)^2)-3.945*x(1)+3.945*x(2)+3.945*x(3)-4.76*x(2)*x(3);
x(3)-7.5*x(2)+5*x(1)*x(2)+5*x(2)*x(3)];
end 
end

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Answer 1

Torsten 2022-6-6

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https://ww2.mathworks.cn/matlabcentral/answers/1734530-three-nonlinear-equation-with-initial-guess#answer_979785

在 MATLAB Online 中打开

fun = @(x,y,z)[-0.06*(x^2)-1.06*(z^2)+3.18*x+3.18*z+1.59*y-2.06*x*y-3.12*x*z-2.385-1.06*y*z;2.63*(x^2)-1.63*(y^2)-2.63*(z^2)-3.945*x+3.945*y+3.945*z-4.76*y*z;z-7.5*y+5*x*y+5*y*z];
u0=[0; 0; 0];
[sol,fval]=fsolve(@(u)fun(u(1),u(2),u(3)),u0)
Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.
sol = 3×1
    0.7079
    0.1909
    0.3868
fval = 3×1
1.0e-10 *

   -0.0873
    0.4509
    0.4931

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Answer 2

Bjorn Gustavsson 2022-6-6

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https://ww2.mathworks.cn/matlabcentral/answers/1734530-three-nonlinear-equation-with-initial-guess#answer_979725

Have a look at the help and documentation of fsolve. That should be the function for this task

HTH

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Answer 3

Walter Roberson 2022-6-6

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https://ww2.mathworks.cn/matlabcentral/answers/1734530-three-nonlinear-equation-with-initial-guess#answer_979800

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with the symbolic toolbox you can find 8 solutions including a complex conjugate pair. The real solutions are approximately

7079    0.1909    0.3868
0375    0.5366    1.0654
9235   -0.3927    1.1749
6229   -0.5919    1.3247
   -0.4412   -3.4575    2.0604
0323   -0.6798    2.0795

As you start from 0,0,0 the implication is that negative components are valid