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MathGroup Archive 2006

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Re: RSolve and known indexed variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72300] Re: RSolve and known indexed variables
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Tue, 19 Dec 2006 06:35:21 -0500 (EST)
  • References: <acbec1a40612181237t1539cdayed9c0eda52db15e9@mail.gmail.com>

BTW, lever[i] is the "known indexed variable" -- it has an index, but
does not need to be RSolved.

On 12/18/06, Chris Chiasson <chris at chiasson.name> wrote:
> Here is an attempt to solve a recurrence relation for the moment[i] at
> particular parts of a beam under constant shear. The index is i.
> lever[i] stands for the length of a particular section of the beam.
>
> I would specify the "initial" condition for the moment at index 1, but
> I want to show a problem into which I've run.
>
> RSolve[{moment[i+1]\[Equal]moment[i]+shear*lever@i,
>     moment[10]\[Equal]someMoment},{moment[i]},i]
>
> {{moment[i] -> someMoment - Sum[shear*lever[K$35], {K$35, K$36, 9}] +
> Sum[shear*lever[K$35], {K$35, K$36, -1 + i}]}}
>
> Notice that the output includes two sums, both with an index of K$35.
> However, the range of the sums start at K$36. K$36 has no value. From
> looking at the output, I would guess that K$36 should have the value
> 10 (the index at which I gave the initial condition for the moment).
>
> For now: I will try to work around this by specifying my own generated
> parameter and then detecting the appropriate Sum structures to find
> the variable to replace.
>
> I have also run into a problem where RSolve returns the input and an
> RSolve::deqx error message if the input has one of these "known
> indexed variables", even though the problem is actually separable (the
> second part of the separate computation is shown above):
>
> RSolve[{moment[10] == someMoment, shear[10] == someShear, moment[1 +
> i] == moment[i] + lever[i]*shear[i],
>   shear[1 + i] == shear[i]}, {shear[i], moment[i]}, i]
>
> So, uh, do you have any suggestions for making Mathematica handle the
> combined problem? Do you have any methods for making Mathematica not
> produce the K$36 variable in the output?
>
> Note: This is one of the few times I have ever attempted to use
> RSolve, and probably the first time in more than a year. I could
> easily be using it incorrectly.
>
> Second note: From the help browser documentation, it appears RSolve
> was moved into the kernel from RSolve.m beginning with version 5, so
> anyone with a version 4.x could probably view a copy of the source
> code that is probably quite similar to what the internal code now
> uses. I lack such a copy.
>
> --
> http://chris.chiasson.name/
>


-- 
http://chris.chiasson.name/


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