Well, I did know about save command but I was just trying to find out if there is anything more efficient, meaning "gathering all the data in one maplesheet under one file/folder" kind of thing as in Matlab.
Thank you, though.
Gurs

Thank you , Scott.
However, to be able to use optimization commands, you need to define some constraints! I do not need to find numerical values.I need to find an equation that will give the minimum of this integral (Euler-Lagrange equation if I am not wrong). For instance, if you have a polynomial function that you want to minimize with respect to one of the variable, you just differentiate the function wrt that variable and equate it to zero. You cannot do the same for the integral functions.
Thanks anyway.
Gurs

I forgot to define the parameters in the integral:
z is the independent variable and P(z) is the dependent variable, a, b, c, d, e, f, g, h, L are constants.

Hi again,
Isn't there anybody that can help me with this? Allan?
To make it more specific:
integrate((a*z+b)*P(z)^2+(c*z+d)*P(z)^4+(e*z+f)*P(z)^6+(g*z+h)*diff(P(z),z)^2, z=0..L)
How do you find the minimization equation?
Thanks
Gurs

I am quite confused about it right now. I kind of understand what you are saying and when I tried one of the bcs as P(8e-8)=0.0635 which is the right hand side value of the matlab solution and the other one as D(P)(8e-8)=0, I also got the oscillatory plot!
I have to look at the eq again.I was pretty sure it was right, I guess it is not!
Allan, you helped enormously. Thank you so very much! I will be back!:)
Gurs

Yes, Allan, the "exact" problem is as you put in your previous reply. I double checked. I apologize again for my mistake...
Thank you very much...
G.

When I first typed the eq, I made a mistake! P^6 has to be P^5. Sorry! But it still does not change the result in maple!
G.

Thank you very much, Allan.
I tried to download the maple file, however, I think, there was aproblem uploading it since it appears to be 0 byte. Could you upload it again? I have to see it to be able to follow what you were saying in your reply.
After writing the DE in discrete form, it can also be written in matrix form as M*P=N (M and N are matrices and P is the vector defining the unknown in steps of dz) leaving the polynomial on the right hand side of the eq in order to approach the problem linearly (N vector is composed of the non-linear part of the eq, i.e. aP+bP^3+cP^5). Matlab code uses the Gauss-Seidel iteration to solve the matrix equation.
In order for the code to converge, step values (dz) and number of steps (X) need to be defined accrodingly. I run the code for dz=0.04e-9 and X=1000 (so z=0..4e-8).
I hope I am making sense!
P(z)=0 might be one of the answers as to the sol'n of this eq. but it cannot be the unique answer since it does not make sense for the physical system equivalent of this DE!
I am sending you the matlab plot in ppt format.
Thanks again,
G.
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I just wanted to update the blog. I am still working on the same problem and if anybody can help me with it, it will be great!
Thanks,
G.

Allan, thanks but I cannot follow what you did in your computation. Why did you solve A with respect to z?

I am sorry again...
The correct expression of A is:
A=abs(3.0164e14*z-2.8071e7)*(-0.82500e-2*z+3e-9)^2

You mean a value for P at z=8e-8? No, I do not have a value for that, unfortunately... That would make it a lot easier...
And sorry about the typo...

I forgot to write the BCs:
D(P)(0)=0,
D(P)(8e-8)=0;
Thanks,
G.

As I mentioned before the DE is:
Eq := A*(diff(P(z), z, z))-alpha_z*P(z)-beta_z*P(z)^3-gamma_z*P(z)^6 = 0
with
A:=abs(3.0164*10^14*z-2.8071*10^7)*(-0.82500e-2*z+3.*10^(9()^2;
alpha_z:=3.0164*10^14*z-2.8071*10^7;
beta_z:=9.9000*10^15*z-5.400*10^8;
gamma_z:=6.6e9 (taken as constant for now)
Trying to find P(z)...
And yes, P(z)=0 at all z's is probably one of the solutions of the DE but that is not one I am looking for as you mentioned.
Any help is very much appreciated!
G.