"Declaring" a vector for NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg70734] "Declaring" a vector for NDSolve*From*: Eric Poolman <emp35 at email.med.yale.edu>*Date*: Wed, 25 Oct 2006 01:40:00 -0400 (EDT)

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