Re: "Declaring" a vector for NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg70766] Re: "Declaring" a vector for NDSolve
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 26 Oct 2006 02:39:29 -0400 (EDT)
• References: <ehmu5d\$sf7\$1@smc.vnet.net>

```Hi,

S = T[t];
ModelEqs = {T'[t] == S, T[0] == {0, 0}}
sol = NDSolve[ModelEqs, {T}, {t, 0, 1}]
tmp = T /. sol[[1]]

tmp[t] /. t -> 0.5

and I'm not able to understand your problem.

Eric Poolman wrote:
> Hello,
>
> I am trying to use Mathematica to solve a set of differential
> equations in an epidemiological model (of sexually-transmitted disease.)
>
> I have been using NDSolve on a system that consists of the following
> two equations:
>
> P'[t]=A.P[t],
> P[0]={0.9, 0.1, ...}
>
> Where P is a vector and A a matrix. Initial efforts with a simple A
> went fine (Mathematica gives an error, "Part :: partw:: Part 2 of P
> [t] does not exist," but it still produces a correct interpolating
> function (verified by solving the simple system with each equation
> written out separately.))
>
> I am now complicating the matrix, A, by including in some of its
> cells functions of P[t]. In particular, some of the terms in A will
> include P[t][[1]] through P[t][[9]].  While P[t][[2]] and higher
> terms are handled "correctly" (I get the error message, but it does
> not interrupt the solving process), P[t][[1]] is not.  P[t][[1]] is
> immediately evaluated as t.
>
> I have the following simplified formulation which shows the issue:
>
> S = {T[t][[1]], T[t][[2]]}
> ModelEqs = {T'[t] == S, T[0] == {0, 0}}
> sol = NDSolve[ModelEqs, {T}, {t, 0, 1}]
> T[1] /. sol
>
> S Evaluates immediately to {t,T[t][[2]]}, which then leads to the
> final line evaluating to {{0.5,0}}, rather than {{0,0}} as it should.
>
> My naive thought is that I need to be able to declare T[t] as a
> vector, so that  T[t][[1]] is not immediately evaluated. I do not
> know if that is a reasonable approach, or if that would work (or how
> to do it.)
>
> I am attempting to write out the program flexibly enough to handle
> varying numbers of diseases (and thus varying dimensions for the
> matrices), and would much prefer not to write out the equations if I
> can do this generally.  If worst came to worst, I suspect I could use
>
> subscripts instead of indices and generate each equation, but the
> matrix solution would be much more elegant (excepting this one issue.)
>
> Thanks in advance; any guidance is appreciated.
>
> Eric
>
> --------------------------------
> Eric Poolman, MD, MBA
> Post-doctoral Fellow
> Epidemiology of Microbial Diseases
> Yale School of Medicine
> 60 College Street, Room 147
> New Haven, CT 06520-8034
> eric.poolman at yale.edu
> 203-589-8925 cell
>
>

```

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