b*y
2 楼
I don't know if it worthes to do higher order
RK at all.
【在 m****n 的大作中提到】
: 请推荐一个常用的格式。
: 如果你有8阶精度的，更好。
RK at all.
【在 m****n 的大作中提到】
: 请推荐一个常用的格式。
: 如果你有8阶精度的，更好。
m*n
3 楼
Surely, it is needed in some scientific calculations. I can give you examples.
J. Chem. Phys. 116, 538 (2002)
Sympletic Integration of Classical Trajectories: A case study
Ch. Schlier and A. Seiter.
【在 b*****y 的大作中提到】
: I don't know if it worthes to do higher order
: RK at all.
J. Chem. Phys. 116, 538 (2002)
Sympletic Integration of Classical Trajectories: A case study
Ch. Schlier and A. Seiter.
【在 b*****y 的大作中提到】
: I don't know if it worthes to do higher order
: RK at all.
h*o
4 楼
我觉得可以自己推呀, hoho...
【在 m****n 的大作中提到】
: 请推荐一个常用的格式。
: 如果你有8阶精度的，更好。
【在 m****n 的大作中提到】
: 请推荐一个常用的格式。
: 如果你有8阶精度的，更好。
w*d
5 楼
sometimes not so easy to get a good high order scheme.
As I remember, the exist highest A-stable(?) RK scheme is
6th order.
If you have some special requirement, e.g. the speed,
the robustness, it is even harder to get
a good one. I once used the 4th order A-stable RK scheme
with only 3 stages. It worked very well sometimes. But for some
problems, the round-off error just killed the solution.
some useful references:
general RK:
Solving ordinary differential equations :
Hairer, E. (Er
【在 h***o 的大作中提到】
: 我觉得可以自己推呀, hoho...
As I remember, the exist highest A-stable(?) RK scheme is
6th order.
If you have some special requirement, e.g. the speed,
the robustness, it is even harder to get
a good one. I once used the 4th order A-stable RK scheme
with only 3 stages. It worked very well sometimes. But for some
problems, the round-off error just killed the solution.
some useful references:
general RK:
Solving ordinary differential equations :
Hairer, E. (Er
【在 h***o 的大作中提到】
: 我觉得可以自己推呀, hoho...
r*r
6 楼
^^^^^^^^^
it is SSP instead of A-stable.
As for A-stable, RADAU, developed
by Hairer (2002), uses A-stable
implicit RK method of variable
orders (between 5, 9 and 13).
Numerical experiments show that,
for stiff problems
【在 w**d 的大作中提到】
: sometimes not so easy to get a good high order scheme.
: As I remember, the exist highest A-stable(?) RK scheme is
: 6th order.
: If you have some special requirement, e.g. the speed,
: the robustness, it is even harder to get
: a good one. I once used the 4th order A-stable RK scheme
: with only 3 stages. It worked very well sometimes. But for some
: problems, the round-off error just killed the solution.
: some useful references:
: general RK:
w*d
7 楼
i c. The paper I read was published before 2002.
【在 r*r 的大作中提到】
:
: ^^^^^^^^^
: it is SSP instead of A-stable.
: As for A-stable, RADAU, developed
: by Hairer (2002), uses A-stable
: implicit RK method of variable
: orders (between 5, 9 and 13).
: Numerical experiments show that,
: for stiff problems
【在 r*r 的大作中提到】
:
: ^^^^^^^^^
: it is SSP instead of A-stable.
: As for A-stable, RADAU, developed
: by Hairer (2002), uses A-stable
: implicit RK method of variable
: orders (between 5, 9 and 13).
: Numerical experiments show that,
: for stiff problems
t*o
8 楼
又多学一点
偶最多只用4阶R-K， 一直认为R-K公式是固定的，
u* = u^0 + dt*...
u** = u* + dt*...
想要多精度就是多写几次， u******, 系数不同而已
HOHO
【在 r*r 的大作中提到】
:
: ^^^^^^^^^
: it is SSP instead of A-stable.
: As for A-stable, RADAU, developed
: by Hairer (2002), uses A-stable
: implicit RK method of variable
: orders (between 5, 9 and 13).
: Numerical experiments show that,
: for stiff problems
偶最多只用4阶R-K， 一直认为R-K公式是固定的，
u* = u^0 + dt*...
u** = u* + dt*...
想要多精度就是多写几次， u******, 系数不同而已
HOHO
【在 r*r 的大作中提到】
:
: ^^^^^^^^^
: it is SSP instead of A-stable.
: As for A-stable, RADAU, developed
: by Hairer (2002), uses A-stable
: implicit RK method of variable
: orders (between 5, 9 and 13).
: Numerical experiments show that,
: for stiff problems
d*q
9 楼
taylor的
一种降阶形式
化为代数计算。。
不过用8阶也。。。【 在 twoxiao (老大,一点通) 的大作中提到: 】
一种降阶形式
化为代数计算。。
不过用8阶也。。。【 在 twoxiao (老大,一点通) 的大作中提到: 】
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