Please be more precise about what you want.

@acer  I understand. Thanks. I might ask some more questions about this sometimes. 

@acer  I understand. Thanks. I might ask some more questions about this sometimes. 

Wow ! that's great. thanks very much. I'm an ameture user, therefore "CodeTools" is new to me, also I don't understand some parameters inside the procedure for EnergyDensity. 

"epsilon" is machine epsilon, right ?

But what is _dO( or is it zero ?)1amc method ?

Aso when I run your worksheet , my version can't work with "Usage", it says : "Error, Usage is not a command in the CodeTools package."

Please note that I use Maple 13, and you made your worksheet using newer version, therefore your code is essentially useless for me because with CodeTools package and usage command I have to find the roots. Please give me a command that can work with Maple 13.

Anyway, thanks again.

Wow ! that's great. thanks very much. I'm an ameture user, therefore "CodeTools" is new to me, also I don't understand some parameters inside the procedure for EnergyDensity. 

"epsilon" is machine epsilon, right ?

But what is _dO( or is it zero ?)1amc method ?

Aso when I run your worksheet , my version can't work with "Usage", it says : "Error, Usage is not a command in the CodeTools package."

Please note that I use Maple 13, and you made your worksheet using newer version, therefore your code is essentially useless for me because with CodeTools package and usage command I have to find the roots. Please give me a command that can work with Maple 13.

Anyway, thanks again.

@Jarekkk 

Thanks a lot for your discussion.

@Jarekkk 

Thanks a lot for your discussion.

Same equns are repeated, it's not an error, it simply means that the equations in the system are not linearly independent -- Linear Algebra 101. How do you know they don't hold together, I didn't give you any details on how I get the system. The bottom line is that there is no error in the system.

Same equns are repeated, it's not an error, it simply means that the equations in the system are not linearly independent -- Linear Algebra 101. How do you know they don't hold together, I didn't give you any details on how I get the system. The bottom line is that there is no error in the system.

Sorry, I don't understand the IODE.mw, it's like the same ws that I attached, with some modifications and d=3. Exactly what I supposed to look at ? It has nothing to do with integro-DE.

Thanks anyway.

Sorry, I don't understand the IODE.mw, it's like the same ws that I attached, with some modifications and d=3. Exactly what I supposed to look at ? It has nothing to do with integro-DE.

Thanks anyway.

Some things should be noted here:

1)The numerical integration is over x, and the ODE is for t, so the integration should not be a problem- I think, but I may be wrong.

2)The solutions should be exponential curves, for a(t)=exp(t)- the EnergyDensity are evaluated and plotted- see: ed_vs_t.pdf

3)For d=4, the exact solutions for EnergyDensity and the ODE exist, It can be done manually (analytically) and I did.  

Well, my source is unavailable, this is why I asked my question here in the first place.

Pardon my naiveness please, what I'm thinking is something like this:

If Maple (using some package, I don't know which package would that be) can find Christoffel symbols, Ricci tensors etc, by using ds^2  directly, then in ds^2 I can use sum() command and assume that n>0. But I still have to deal with the issue that i is coordinate label, not power and it makes thing complicated.

Thanks anyway.

Well, my source is unavailable, this is why I asked my question here in the first place.

Pardon my naiveness please, what I'm thinking is something like this:

If Maple (using some package, I don't know which package would that be) can find Christoffel symbols, Ricci tensors etc, by using ds^2  directly, then in ds^2 I can use sum() command and assume that n>0. But I still have to deal with the issue that i is coordinate label, not power and it makes thing complicated.

Thanks anyway.

Thanks a lot.