@Thomas Richard 

Thanks. 

@koreff 

Upload your maple work sheet using the up green arrow.

@umar khan 

If you meant to say that your v(r)

v:=r->((1/4*(3*(1-(R/a)^2)^.5-(1-(r/a)^2)^.5))/2);

then 

plot(exp(v(r)/2),r=0..2e6);

will give you the desired plot.

I do not see v(r). and certainly no r anywhere in your sheet.

restart
v:=(1/4*(3*(1-(R/a)^2)^.5-(1-(r/a)^2)^.5));
R:=1:a:=1:

plot(exp(v/2),r=0..2);
 

@tomleslie 

The issue was with the Digits.

For defualt digits, P(r) = 

4.449669928*10^27

Digits:=50:

6.657168...*10^(-13)

Digits:=100:

7.2427...*10^(-64)

@tomleslie 

When I use the value of `r` for which you claim that P(r)=0, I get

fsolve(rhs(sol), r = -5*10^6 .. 0, fulldigits)

evalf(subs(r=%,rhs(sol)));

4.449669928*10^27+0.*I

Like your previous post, you have repeated the mistakes.

1. There is no such thing as `refresh` instead you should use `restart`

2. You should not assign value to `Pi`. It is pre-defined in Maple with a Caps 'P'. 

Now coming to your question which is unclear. Do you want to find the boundary condition first  and then solve the system of ODE's?

@vv 

I got the book but unable to see the code for FDM. Could you please be more specific, like page number?

@vv 

The second part of my question (second question) is, Is there a more sophisticated way to implement FDM than the one i used?

@tomleslie 

We can avoid F(infinity) by using `Sum` instead of `sum` but still I am unable to reproduce any plot.

Upload your Maple worksheet using the Up green arrow.

@hitstudent 

Use up green arrow to upload your Maple worksheet.

@YOUNESOMMANE 

Now Edit your question and add your maple file. And also delete all the comments.

This will save some space and time.

Younes_Algo_Hellinger.mw

Apart from some basic syntax issues, the numerical PDE solve is unable to proivde a solution. But still you can have a general solution only for theta.

PDEs_solve.mw

@Thomas Richard 

You are right about `Pi` but the function is correctly defined the Maple way.

As 2D-Maths input phi[2](xi):= sin(2*Pi*xi)^3 is the same as a Maple-input of phi[2]:=xi-> sin(2*Pi*xi)^3.

Question_(1).mw