coupled eqns in NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg48883] coupled eqns in NDSolve*From*: "Stergios J. Papadakis" <stergios.papadakis at jhuapl.edu>*Date*: Tue, 22 Jun 2004 05:31:20 -0400 (EDT)*Organization*: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA*Sender*: owner-wri-mathgroup at wolfram.com

Dear group, Do you know if NDSolve can solve two coupled equations with different numbers of variables? It looks to me like the algorithm should be able to do so, but that there is some test beforehand that doesn't let it start (it just returns a message that "the length of the derivative operator... is not the same as the number of arguments"). Do you think I just have the syntax wrong or can NDSolve not do this? I am trying to solve 2 coupled differential equations using NDSolve. One is a function of time t only, z[t] (the harmonic oscillator equation) and the other is a function of position x and time t, T[x,t] (the heat equation). They are coupled because the harmonic oscillator solution z[t] is a boundary condition on the heat equation, and the heat equation solution at one particular location L on the boundary, T[L,t], modifies the spring constant of the harmonic oscillator equation. I got NDSolve to work by artificially making z a function of x and t (z[x,t]), knowing that only z[L,t] really had any meaning for me. However, this takes much longer than I think it needs to because it is solving for z[x,t] everywhere along x when it doesn't really need to. I ignore everything except z[L,t] anyway. What are your thoughts? Thanks, Stergios