Hi all!

I do a small calculation and get a system of 6

nonlinear equations.

And "n" is the degree of the equation is float.

Here are the calculations that lead to the system.

restart;

with(DirectSearch):

B:=1:

q:=1:

l:=1:

n:=4.7:

V:=0.05:

N:=1200:

kappa:=Vector(N+1,[]):

theta:=Vector(N+1,[]):

u:=Vector(N,[]):

M:=Vector(N,[]):

Z:=Vector(N,[]):

M_F:=q*(6*l*(z-l)-z^2/2):

M_1:=piecewise((z<l), l-z, 0):

M_2:=piecewise((z<2*l), 2*l-z, 0):

M_3:=piecewise((z<3*l), 3*l-z, 0):

M_4:=piecewise((z<4*l), 4*l-z, 0):

M_5:=piecewise((z<5*l), 5*l-z, 0):

M_6:=6*l-z:

M_finish:=(X_1,X_2,X_3,X_4,X_5,X_6,z)->M_1*X_1+M_2*X_2+M_3*X_3+M_4*X_4+M_5*X_5+M_6*X_6+M_F:

kappa_old:=0:

theta_old:=0:

u_old:=0:

M_old:=0:

step:=6*l/N:

u[1]:=0:

kappa[1]:=0:

theta[1]:=0:

for i from 2 to N do

z:=i*step:

kappa_new:=kappa_old+B/V*(M_finish(X_1,X_2,X_3,X_4,X_5,X_6,z))^n*step:

theta_new:=theta_old+1/2*(kappa_old+kappa_new)*step:

u_new:=u_old+1/2*(theta_old+theta_new)*step:

Z[i]:=z:

kappa[i]:=kappa_new:

theta[i]:=theta_new:

u[i]:=u_new:

kappa_old:=kappa_new:

theta_old:=theta_new:

u_old:=u_new:

end do:

** So,my system:**

** u[N/6]=0;**

** u[N/3]=0;**

** u[N/2]=0;**

** u[2*N/3]=0;**

** u[5*N/6]=0;**

** u[N]=0;**

I want to ask advice on how to solve the system.

I wanted to use Newton's method, but I don't know the initial values X_1..X_6.

Tried to set the values X_1..X_6 and to minimize the functional

Fl:=(X_1,X_2,X_3,X_4,X_5,X_6)->(u[N/6])^2+(u[N/3])^2+(u[N/2])^2+(u[2*N/3])^2+(u[5*N/6])^2+(u[N])^2:

with the help with(DirectSearch):

GlobalOptima(Fl);

But I don't know what to do next

Please, advise me how to solve the system! I would be grateful for examples!