delayed (numerical) matrix inversion in NDSolve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg131625] delayed (numerical) matrix inversion in NDSolve?*From*: "vadim.oganesyan at gmail.com" <vadim.oganesyan at gmail.com>*Date*: Fri, 13 Sep 2013 00:35:15 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hi, How do I get NDSolve to solve coupled ODE system in the form P[v].v'==Q[v]? P[v] and Q[v] contain all kinds of trig functions etc. but I am more or less guaranteed the existence of nice smooth solutions v, as well as 1/P for the problem at hand. As far as I can tell the difficulty is in the way NDSolve prepares the equations before iterating (using Solve, apparently?!?!): for small sizes <=4 NDSolve works without a hitch but for larger ones it hangs up. I have tried asking it to solve v'==(P)^(-1)Q and use delayed inverse to try and force numerical evaluation of the right-hand-side (which is easy) but no luck. I gave up and hand-coded a simple RK4 and/or Euler and it worked without a hitch, so I am pretty sure the problem is in the NDSolve being stubborn on the initial step. thoughts? thanks,v