Three nonlinear equation with initial guess

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Nihal Yilmaz
Nihal Yilmaz on 6 Jun 2022
Commented: MOSLI KARIM on 12 Aug 2022 at 7:04
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 Comment
MOSLI KARIM
MOSLI KARIM on 12 Aug 2022 at 7:04
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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Answers (3)

Torsten
Torsten on 6 Jun 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 on 6 Jun 2022
Have a look at the help and documentation of fsolve. That should be the function for this task
HTH

Walter Roberson
Walter Roberson on 6 Jun 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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