@tomleslie 
Dear Sir,

How can I turn the three parametric equations (Eq22, Eq33, Eq44 in the attached file) into an equation in term of phi[d0] and delta[d]?
I want to get an equation similar to C1*phi[d0]+C2*delta[d]=0 where C1 and C2 are known coefficients.
Assume that u[i10], u[i20], phi[d0] and delta[d] are the only unknowns in mentioned equations and the rest of parameters (for example, alpha, delta[i],...)are known.

Equation.mw

@acer 
 

Hi,

What can be done when a question is not answered but sent back to other people??

@raj2018
Dear  tomleslie ,
Are the above parameters sufficient to solve the set of NL equations?

@tomleslie 

Sorry! 
I have been inaccurate when writing. In fact, using equations 1-4 and assuming that  alpha=0.01, delta[d]=1e-4 and the range of changes in delta[i] = 10e-5..10, I want to plot the variation of u[i01],u[i02] and phi[d0] versus delta[i].

A paragraph of the article is as follows:

"The non-linear equations (1)-(4) constitute a complete set of equations enabling the computation
of delta[e], phi[d0],u[i10], and u[i20] for different  parameters such as alpha=0.01 and delta[d]=1e-4."

@tomleslie 
Hi,
As you said, Equation 1 had a problem, and now I have solved the problem, and the number of equations is consistent with the unknowns. Please see the attachment and help solve the equations.

Regards,

H.mw

@tomleslie 

Similar to your worksheet, I tried to write my equations in the form    ” f(u[i10], u[i10], phi[d0])=delta[d]”

Equations 1 and 2 were written in this form easily, but I couldn’t do that for equation 3  due to following error:

`[Length of output exceeds limit of 1000000]`

Solve.mw

@tomleslie 
Thank you for your reply. I'll try to solve my Eqs. with your comperhensive response. 

Can I have your email address?

r.choupta@gmail.com

@tomleslie 

 

@tomleslie 
I tried to sent the article file to you, but I couldn't. However, what is your opinion about this assumption to plot the figures?

Assuming that delta[d] varies from 10^(-6) to 10^(-3), we have 3 equations and 3 unknowns u[1i0], u[2i0] and phi[d0]. Therefore, I solve the set of equations several times by a loop to find "u[i10], u[i20] and phi[d0]" for each step of the loop.

For example,

#%%%%%%%%%%%%%%%%%%%%
for delta[d] from 10^(-6) by 10^(-6) to 10^(-3) do
sys:=eval([Eq2a,Eq3,Eq4],[delta[i]=0.5,alpha=0])
fsolve(sys)
print delta[d], u[i10],u[i20],phi[d0]
end do
#%%%%%%%%%%%%%%%%%%%%


How do I do this by Maple and how can I extract data for ploting u[1i0] vs delta[d],....?
Now,

@tomleslie 
I sent you the article. Please see the attached file.(see the last paragraph in Sec. II and the curves in Sec. III)

[copied without permission, deleted by moderator]

According to the above message, How to send the article file to you?
Please, see the following link:

https://doi.org/10.1063/1.4967763

@tomleslie 

How do you think the author of the article was able to draw the relevant figure? The article only mentions these four equations and parameters that I wrote. The exact phrase of the article is:

The non-linear equations (1), (2), (3), and (4) constitute
a complete set of equations enabling the computation
of  delta[e], phi[d0], u[i10], and u[i20] vs delta[d] for different physical parameters !!

@tomleslie 

You are right!
According to the figure I sent, it seems that the delta change interval is known, so he/she changed the delta value in a loop from 10^-6 to 10^-3 and solved three other equations for each delta value. How do I do this with Maple?

@tomleslie 
Thank you for your help, Sir!

@acer 
Thanx!

@Carl Love 

Yes. They should be positive

@tomleslie 

Many Thanks.

I'll appreciate if assist me to answer two following questions:

1- Since my question was about how to solve a first-order ODE [diff(A(x),x)^2+V(A(x))=0],  I ignored one of the ICs, but I encountered Maple an error message ('unable to convert to an explicit first-order system'). How can I remove it?

2- How can I find another point (except x=0) like x1<>0 where A(x) satisfies the following two conditions in that point?

A(x1)=0

dA(x1)/dx=0.

Sincerely.