Re: Re: NDSolve[] with nested If[] and Piecewise[] usage:

*To*: mathgroup at smc.vnet.net*Subject*: [mg91427] Re: [mg91403] Re: NDSolve[] with nested If[] and Piecewise[] usage:*From*: DrMajorBob <drmajorbob at att.net>*Date*: Thu, 21 Aug 2008 04:16:04 -0400 (EDT)*References*: <25682308.1219270716763.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

I'd use one of these: sep = 1; len = 3; wdef1[t_] := y[t]; wdef2[t_] := y[t]; val1 = 50; val2 = 20; xv = 1/2; yv = 1/5; Clear[t] funifcase2b[t_] = If[0 <= t < sep/len, val1 + val1 xv yv^2 (wdef1[t]) Sin[t], If[sep/len <= t <= (2 sep)/len, val1 + val2 + val1 xv yv^2 (wdef1[t]) Sin[t] + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], If[(2 sep)/len < t <= 1, val2 + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len]]]] /. If -> if /. if -> If // PiecewiseExpand \[Piecewise] { {20 - Sin[1/3 - t] y[t], 2/3 < t <= 1}, {50 + Sin[t] y[t], 0 <= t < 1/3}, {70 - Sin[1/3 - t] y[t] + Sin[t] y[t], 1/3 <= t <= 2/3} } or funifcase3b[t_] = Piecewise[{{val1 + val1 xv yv^2 (wdef1[t]) Sin[t], 0 <= t < sep/len}, {val1 + val2 + val1 xv yv^2 (wdef1[t]) Sin[t] + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], sep/len <= t <= (2 sep)/len}, {val2 + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], (2 sep)/len < t <= 1}}] \[Piecewise] { {50 + Sin[t] y[t], 0 <= t < 1/3}, {70 - Sin[1/3 - t] y[t] + Sin[t] y[t], 1/3 <= t <= 2/3}, {20 - Sin[1/3 - t] y[t], 2/3 < t <= 1} } Evaluate doesn't evaluate everything, because If has the attribute HoldRest; I defeated that by replacing If with if, then replacing if with If. Then I created a Piecewise equivalent via PiecewiseExpand. Piecewise didn't work as you expected (I think) because you used SetDelayed (:=) where you needed Set (=). The two definitions above are equivalent functions, but one could be faster than the other, depending on what intervals x is more likely to inhabit. You want the most likely interval first, least likely last, etc. That's probably a very slight improvement at best, however. Bobby On Wed, 20 Aug 2008 03:05:01 -0500, Gopinath Venkatesan <gopinathv at ou.edu> wrote: > Hello Jean, > > Thank you for replying me. > > I use v1[t], v2[t], v3[t], phi[t](symbol phi) and vi[i][j] as unknown > functions (you can say variables, thats why I introduced 5 equations and > 10 initial conditions). > > I sincerely believe there should not be any problem as such in doing so. > The last time I posted, Oliver and DrMajorBob, both pointed out that the > parts of the expressions inside the If[] remain unevaluated. For that I > used Evaluate[] for each of the parts/expressions inside If[] and it > worked - produced same result as the Piecewise[] did. > > Now for this case (which is very similar), the Piecewise[] itself did > not work. Thats why I am clueless. > > Just for your reference, please see the code at the bottom: After > putting Evaluate[] inside for one of the problem, I was able to solve > it. But this is not the problem I am looking to solve - it is already > solved from suggestions given by Oliver and DrMajorBob. Please see my > previous post that starts with "Sometime back I posted this question on > the ..." posted on August 19. You can browse the bottom for the code > that I am looking for your help and suggestions to solve. Thank you. > > (* Working sample code starts here *) > > sep = 1; > len = 3; > wdef1[t_] := y[t]; > wdef2[t_] := y[t]; > val1 = 50; > val2 = 20; > xv = 1/2; > yv = 1/5; > funifcase2[t_] := > Evaluate[If[Evaluate[0 <= t < sep/len], > Evaluate[val1 + val1 xv yv^2 (wdef1[t]) Sin[t]], > Evaluate[ > If[Evaluate[sep/len <= t <= (2 sep)/len], > Evaluate[ > val1 + val2 + val1 xv yv^2 (wdef1[t]) Sin[t] + > val2 yv xv^2 (wdef2[t]) Sin[t - sep/len]], > Evaluate[ > If[Evaluate[(2 sep)/len < t <= 1], > Evaluate[ > val2 + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len]]]]]]]]; > > (* previous definition of funifcase2[t] -- not working *) > > (* funifcase2[t_] := > If[0 <= t < sep/len, val1 + val1 xv yv^2 (wdef1[t]) Sin[t], > If[sep/len <= t <= (2 sep)/len, > val1 + val2 + val1 xv yv^2 (wdef1[t]) Sin[t] + > val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], > If[(2 sep)/len < t <= 1, > val2 + val2 yv xv^2 (wdef2[t]) Sin[t - sep/len]]]]; *) > > funifcase3[t_] := > Piecewise[{{val1 + val1 xv yv^2 (wdef1[t]) Sin[t], > 0 <= t < sep/len}, {val1 + val2 + > val1 xv yv^2 (wdef1[t]) Sin[t] + > val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], > sep/len <= t <= (2 sep)/len}, {val2 + > val2 yv xv^2 (wdef2[t]) Sin[t - sep/len], (2 sep)/len < t <= > 1}}]; > Chop[Table[funifcase2[t], {t, 0, 1, 0.1}]] > Print["compare values, just to check the correctness of equation \ > above"]; > Chop[Table[funifcase3[t], {t, 0, 1, 0.1}]] > Print["The definition funifcase2[t] is ", funifcase2[t]]; > Print["The definition funifcase3[t] is ", funifcase3[t]]; > ?funifcase2 > ?funifcase3 > > solifcase2 = > NDSolve[{y''[t] + y'[t] + y[t] - funifcase2[t] == 0, y[0] == 0, > y'[0] == 1}, y, {t, 0, 1}]; > Plot[Evaluate[{y[t], y'[t]} /. solifcase2], {t, 0, 1}, > PlotStyle -> Automatic] > Print["Proceeding to solve the above equation with Piecewise \ > definition"]; > solifcase3 = > NDSolve[{y''[t] + y'[t] + y[t] - funifcase3[t] == 0, y[0] == 0, > y'[0] == 1}, y, {t, 0, 1}]; > Plot[Evaluate[{y[t], y'[t]} /. solifcase3], {t, 0, 1}, > PlotStyle -> {Black, {Red, Dashed}}] > > (* Code ends here *) > > -- DrMajorBob at longhorns.com