I notice that both Rosetta Code scripts - yours and Ric's - pull out
the coefficients (1 2 2 1) from the equation for "Yn+1". From what I
can understand of the Wikipedia page on RK, these are based on a
Simpson's Rule approximation for this "fourth-order" method. Is there
any useful generalization that might proceed from this, say to a
higher-order method, or something? Or are the error terms thought to
be sufficiently small that such a generalization is not considered
useful?
I'd like to find some way to emphasize the generality of the solution
which treats these coefficients as a distinct vector rather than
embedding them into the code the way the other ones do, but I don't
understand the problem domain well enough to know a useful direction
in which to go.
On Fri, May 11, 2012 at 5:04 AM, Aai <agroeneveld...@gmail.com> wrote:
> Because rk4M started also with an accumulating fold, the next version
> will be:
>
> p4=: 1 :(':';'({:y)+6%~+/1 2 2 1*(x*[: u y+(*x&,))/\.1 0.5 0.5,x*u y')
>
> rk4M=: 1 :0
> 'Y0 a b h'=. 4{. y
> (,.[:h&(u p4)@,/\.Y0,~}.)&.|. a+i.@>:&.(%&h) b-a
> )
>
>>
>> (*x&,@{:)
>>
>> was used in an earlier attempt with an accumulating fold. It can be
>> simplified (because of using the faster scan fold) to
>>
>> (*x&,)
>>
>
> --
> Met vriendelijke groet,
> @@i = Arie Groeneveld
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
--
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail
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