Re: Nonautonomous ODEs

*To*: mathgroup at smc.vnet.net*Subject*: [mg72750] Re: Nonautonomous ODEs*From*: dh <dh at metrohm.ch>*Date*: Wed, 17 Jan 2007 07:28:56 -0500 (EST)*Organization*: hispeed.ch*References*: <eoht6m$puv$1@smc.vnet.net>

Hi Virgil, use "Piecewise". E.g. F[t_] := Piecewise[{{1, t < 6}, {0, True}}, 0]; Daniel Virgil Stokes wrote: > I am having a problem with the numerical solution of non-autonomous > ODEs. For example, I have the following code for a simple linear 2nd > order ODE with a forcing function, F[t_] > > Clear[x,t] > a = 36; > b = 12; > c = 145; > t0=0; tmax = 20; > eqn := a x''[t] + b x'[t] + c x[t] == F[t] > F[t_] := 100 Exp[-t/6]Cos[2 t]; > > The following code gives its analytical solution and a plot of the > solution for zero initial conditions, > > soln = DSolve[{eqn,x[0]==0,x'[0]==0},x[t],t]//Simplify > truesoln = x[t]/.soln > Plot[truesoln,{t,t0,tmax}]; > > The numerical solution and its plot can be obtained with, > > soln = NDSolve[{eqn,x[0]==0,x'[0]==0},x[t],{t,t0,tmax}]; > Plot[Evaluate[x[t]/.soln],{t,t0,tmax}]; > > My problem, is that suppose the driving function is a sequence of unit > amplitude rectangular pulses, each with width of 0.3 and having a period > 1.0, then how can F[t_] be defined so that NDSolve can be used to obtain > a numerical solution? > > --V. Stokes >