@dharr 

Thanks so much.

Please see the attachment pdf file.

Is possible to solve differential equations numerically?

Best

EXAMPLE.pdf

@mmcdara 

Thanks so much,

Please see the attachment in this regard.

I provided all of the boundary conditions.

the goal is to solve equations 6-30 to 6-33.

Thanks

EXAMPLE.pdf

@dharr 

How do I resolve the singularity problem?

Thanks. But by consideration of your comment, the problem has not been solved thoroughly!!

@Axel Vogt 

Thanks so much,

How do you estimate singularities points for trial and error ?

@Carl Love 

Thanks so much..

My problem is solved

@gkokovidis 

Thanks .

When I run the second line, the answer is

with(DirectSearch);
                     [GlobalSearch, Search]

What is the problem?

I completed the whole installation step.

Could you guide me on what the problem is? 

@Axel Vogt 

Thanks so much,

How do you find these roots?

@Carl Love 

Could you please explain why DirectSearch does not work? 

I encountered this error:

DirectSearch:-SolveEquations(Eq1=p_o-p_i,Eq2=F_a, AllSolutions);
Error, SolveEquations is not a command in the DirectSearch package
NULL;
Thanks

Fung.mws

@Carl Love 

Thanks, dear Carl,

As I know, this method can guarantee the number of solutions. see more information at '

https://math.stackexchange.com/questions/1415898/pseudo-arclength-continuation-scheme

I installed the DirectSearch package, but I can not use the command 'SolveEquations with option AllSolutions'.

Could you please give me the command that you used?

I read this post and reported that sometimes DirectSearch faces some difficulties. Could you please give your opinion in this regard?

https://www.mapleprimes.com/posts/201020-About-DirectSearch

@Rouben Rostamian  

Thanks so much,

How do we find other roots?

I researched and found out that numerical schemes like Pseudo-arclength continuation scheme can find roots.

Would you happen to be familiar with this method?

Thanks