Re: Re: Diff. Equations with "Changeable" Parameters

*To*: mathgroup at smc.vnet.net*Subject*: [mg51712] Re: [mg51693] Re: Diff. Equations with "Changeable" Parameters*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 31 Oct 2004 01:15:15 -0500 (EST)*References*: <clpsou$abt$1@smc.vnet.net> <200410290739.DAA03443@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

This does not do what you think it does. All you are doing is simply solving the differential equation with f givne by your third definition: f[x_, y_] := x + Sin[t] + 2*y. Your idea, however, is correct, but you need to use the correct syntaxt for a conditional definition of a function. The following does essetnially what you intended to do: (f[x_, y_, t_] /; -1 < y && y < 1 := x + Sin[t] + 1*y)* (f[x_, y_, t_] /; y <= -1 := x + Sin[t] + 0*y; )* (f[x_, y_, t_] /; 1 <= y := x + Sin[t] + 2*y) {f, g} = Flatten[{x, y} /. NDSolve[{Derivative[1][x][ t] == y[t], Derivative[1][y][t] == f[x[t], y[t], t], y[0] == 0, x[0] == 0}, {x, y}, {t, 0, 2*Pi}]] {InterpolatingFunction[], InterpolatingFunction[]} Plot[{f[t],g[t]},{t,0,2Pi}] You can check that this gives the same pair of solutions as given by Curt Fisher's method (using Unitstep). Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/ On 29 Oct 2004, at 16:39, Peter Valko wrote: > You need an initial condition for x as well. > Then a right hand side function definition is handy: > > f[x_, y_] := x + Sin[t] + 1*y; -1 < y && y < 1; > f[x_, y_] := x + Sin[t] + 0*y; y <= -1; > f[x_, y_] := x + Sin[t] + 2*y; 1 <= y; > > NDSolve[{x'[t] == y[t], y'[t] == f[x[t], y[t]], > y[0] == 0, x[0] == 0}, {x[t], y[t]}, {t, 0, 2Pi}] > > The result will be: > {{x[t] -> InterpolatingFunction[{{0., 6.28319}}, <>][t], > y[t] -> InterpolatingFunction[{{0., 6.28319}}, <>][t]}} > > Regards > Peter > > "Krunom Ilicevic" <krunom at hotmail.com> wrote in message > news:<clpsou$abt$1 at smc.vnet.net>... >> I have solved diff. equations in this kind of a way: >> >> NDSolve[{x'[t]=y[t],y[0]=0}, {y'[t]=x+Sin[t]+c*y[t]},{x,y},{t,0,2Pi}] >> >> and parameter c was 1, but how to write this algorithm if c is: >> >> c=0, if y<=-1 >> >> c=1, if -1<y<1 >> >> c=2, if y>=1 >> >> How to include this variable parameter c in my NDSolve method? >> >> >> >> Thanks. > >

**References**:**Re: Diff. Equations with "Changeable" Parameters***From:*p-valko@tamu.edu (Peter Valko)