Three nonlinear equation with initial guess

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Nihal Yilmaz
Nihal Yilmaz el 6 de Jun. de 2022
Comentada: MOSLI KARIM el 12 de Ag. de 2022
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=?
  1 comentario
MOSLI KARIM
MOSLI KARIM el 12 de Ag. de 2022
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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Respuestas (3)

Torsten
Torsten el 6 de Jun. de 2022
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

Bjorn Gustavsson
Bjorn Gustavsson el 6 de Jun. de 2022
Have a look at the help and documentation of fsolve. That should be the function for this task
HTH

Walter Roberson
Walter Roberson el 6 de Jun. de 2022
with the symbolic toolbox you can find 8 solutions including a complex conjugate pair. The real solutions are approximately
0.7079 0.1909 0.3868
0.0375 0.5366 1.0654
0.9235 -0.3927 1.1749
0.6229 -0.5919 1.3247
-0.4412 -3.4575 2.0604
0.0323 -0.6798 2.0795
As you start from 0,0,0 the implication is that negative components are valid

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