NDSolve -- initial conditions
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From: Michael Ederer on 27 Jan 2007 05:21 Hello MathGroup, For computation of initial conditions NDSolve uses somehow the simulation time. For example: ==== equ = {D[x1[t], t] == -10^5 * x1[t], x1[0] == 1}; NDSolve[equ, x1[t], {t, 0, 50}, "SolveDelayed" -> True]; NDSolve[equ, x1[t], {t, 0, 100}, "SolveDelayed" -> True]; --- The first NDSolve (simulation time 50) runs without errors, but the second (simulation time 100) says: "NDSolve::icfail: Unable to find initial conditions which satisfy the residual function within specified tolerances. Try giving initial conditions for both values and derivatives of the functions" === I use NDSolve for numerical simulation of nonlinear, stiff, differential-algebraic equation systems of the form B(x) xdot = f(x) with singular B(x) (Method->IDA). For this reason, I need the SolveDelayed-option and I often have simulation times much larger than the fastest dynamics. This often leads to problems with the above described behavior. To avoid this problem, I divide the whole simulation time into smaller parts by using something like sd=NDSolve`ProcessEquations[..] and NDSolve`Iterate[sd,t1], NDSolve`Iterate[sd,t2],.... with t1<t2<... . However, then I very often get solutions that are non-continuous at t1, t2, ... . So, this is not a good solution. An alternative would be to follow the suggestion in the error message and give initial conditions for the derivatives. Those I would have to compute by using FindRoot. This is annoying, since NDSolve could in principal find initial conditions for a smaller simulation time. I would prefer if I could handle the simulation and the computation of initial derivatives solely using NDSolve. So this is my question: Is there any Option or different mechanism in NDSolve that controls the numeric computation of initial conditions and initial derivatives? Could this option be used to prevent the "NDSolve::icfail" for systems with partly very fast dynamics? Thanks and best regards Michael Ederer P.S.: I use Mathematica 5.0
From: Jens-Peer Kuska on 29 Jan 2007 04:06 Hi, a good reason to update to version 5.2, your example below run without any problems. Regards Jens Michael Ederer wrote: > Hello MathGroup, > > For computation of initial conditions NDSolve uses somehow the simulation > time. > > For example: > ==== > equ = {D[x1[t], t] == -10^5 * x1[t], x1[0] == 1}; > > NDSolve[equ, x1[t], {t, 0, 50}, "SolveDelayed" -> True]; > NDSolve[equ, x1[t], {t, 0, 100}, "SolveDelayed" -> True]; > --- > The first NDSolve (simulation time 50) runs without errors, > but the second (simulation time 100) says: > "NDSolve::icfail: Unable to find initial conditions which satisfy the > residual function within specified tolerances. Try giving initial > conditions for both values and derivatives of the functions" > === > > I use NDSolve for numerical simulation of nonlinear, stiff, > differential-algebraic equation systems of the form > B(x) xdot = f(x) with singular B(x) (Method->IDA). > For this reason, I need the SolveDelayed-option and I often have simulation > times much larger than the fastest dynamics. > This often leads to problems with the above described behavior. > > To avoid this problem, I divide the whole simulation time into smaller parts > by using something like sd=NDSolve`ProcessEquations[..] and > NDSolve`Iterate[sd,t1], NDSolve`Iterate[sd,t2],.... with > t1<t2<... . However, then I very often get solutions that are non-continuous > at t1, t2, ... . So, this is not a good solution. > > An alternative would be to follow the suggestion in the error message and > give initial conditions for the derivatives. > Those I would have to compute by using FindRoot. This is annoying, since > NDSolve could in principal find initial conditions for a smaller simulation > time. I would prefer if I could handle the simulation and the computation > of initial derivatives solely using NDSolve. > > > So this is my question: > Is there any Option or different mechanism in NDSolve that controls the > numeric computation of initial conditions and initial derivatives? > Could this option be used to prevent the "NDSolve::icfail" for systems with > partly very fast dynamics? > > > Thanks and best regards > Michael Ederer > > > P.S.: I use Mathematica 5.0 >
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