Hamiltonian System有什么好的方法吗？ - 未名空间MITBBS历史存档

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Hamiltonian System有什么好的方法吗？

Hamiltonian System有什么好的方法吗？# Computation - 科学计算

g*n2002-03-28 08:03

1 楼

I am just wondering if there is any generally good numerical method for
Hamiltonian System?
I learned some symplectic methods(such as the implicit midpoint rule and
the leapfrog method) , but still they seem not very good.
The problem of symplectic methods is they don't conserve energy.
So I want to know if there is a better method.
Thank you very much.

j*c2002-03-28 08:03

2 楼

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
what do you mean by this? as I know, the most significant feature of
a symplectic integrator is that the energy loss is bound, which mean
it conserves energy during long term integration.

【在 g****n 的大作中提到】

: I am just wondering if there is any generally good numerical method for
: Hamiltonian System?
: I learned some symplectic methods(such as the implicit midpoint rule and
: the leapfrog method) , but still they seem not very good.
: The problem of symplectic methods is they don't conserve energy.
: So I want to know if there is a better method.
: Thank you very much.

K*N2002-03-28 08:03

3 楼

faint, that's exaclty what i am studying now. i will give a presentation
end of this semester. i am reading paper now.
well, u have some points seems not correct for me.
sympletic methods is used for those hamiltonian system, which we will need
to integrate them based on some feature that they conserve energy.
i know implicit midpoint and leapfrog method (kind of mid-point method).
i don't think they are simplicit method.
later if i learn much more, i will post here.
if you are knowing something

【在 g****n 的大作中提到】

K*N2002-03-28 08:03

4 楼

you are right. are you expect of this sympletic method? i got confused
of his post also.

【在 j*c 的大作中提到】

:
: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
: what do you mean by this? as I know, the most significant feature of
: a symplectic integrator is that the energy loss is bound, which mean
: it conserves energy during long term integration.

j*c2002-03-28 08:03

5 楼

no I'm not. I wrote a term paper about symplectic integrator one year ago
for a computation course, and never study further on it thereafter.
Probably I can give you some reference on it if you need

【在 K*****N 的大作中提到】

: you are right. are you expect of this sympletic method? i got confused
: of his post also.