Three nonlinear equation with initial guess
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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 个评论
MOSLI KARIM
2022-8-12
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
回答（3 个）
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)
Bjorn Gustavsson
2022-6-6
0 个投票
Have a look at the help and documentation of fsolve. That should be the function for this task
HTH
Walter Roberson
2022-6-6
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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2022-6-6
2022-8-12
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