Re: recording singularities of NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg80511] Re: recording singularities of NDSolve*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 24 Aug 2007 01:54:12 -0400 (EDT)*Organization*: Uni Leipzig*References*: <fajnb6$pcs$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, you can't use NDSolve[] for singularities, because the numerical solution uses a polynomial approximation for the time dependence. A polynom can never approximate a singularity like 1/t^n and on needs a different solver tha uses rational function approximations, but it is not mutch research done on that solvers and Mathematica has none. Regards Jens Judith Bunder wrote: > Hi, > > I have to solve a system of simultaneous equations and I have to solve them > several times with varying initial conditions. I use something like this: > > Do[{c1 = i/imax, c2 = j /jmax, > sol[i, j] = First@NDSolve[eqns, coup, {t, 0, > 100}]}, {j, 1, 5}, {i, 1, 5}] > > So, I solve the the problem 25 times with 5 different j values and 5 different > i values. The variables c1 and c2 are the variable initial conditions. I have > no problems with this part. > > My problem is, sometimes the solution diverges. This is good, I'm looking for > divergent points. But, I want some method of recording where the solution > diverges. I get the warning messages: > > NDSolve::ndsz At t=18.28484703670573` step size is effectively zero; > singularity or stiff system suspected. > > so I could manually record this value of t. But, this isn't practical as > several of my 25 solutions are usually divergent (and I also need to record > the value of i and j). Is there any way to define something like t-div[i,j] > which will record all these points where my solution diverges? > > Thanks in advance, > Judy >