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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90760] Re: NDSolve[] with nested If[] and Piecewise[] usage:
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 23 Jul 2008 05:57:53 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <g6448s$djv$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

Clear[funifcase1]
funifcase1[t_?NumericQ] :=
   If[0 <= t < 1/3, Sin[t],
    If[1/3 <= t <= 2/3, -1, If[2/3 < t <= 1, Cos[t]]]];
Print["funifcase1 is given by ", funifcase1[t]];
solifcase1 =
   NDSolve[{y''[t] + y'[t] + y[t] - funifcase1[t] == 0, y[0] == 0,
     y'[0] == 1}, y, {t, 0, 1}];
Plot[Evaluate[{y[t], y'[t]} /. solifcase1], {t, 0, 1},
  PlotStyle -> {Black, {Red, Dashed}}]

work fine, what is your problem ?

Regards
   Jens

Gopinath Venkatesan wrote:
> Hello Mathematica Friends,
> 
> I am stuck with this problem, where I use NDSolve[] to solve a nested If[] statement. The use of Piecewise[] solves with no problem, but wanted to know if I can solve the If[] part as well.
> 
> The sample code (just for demo) is shown below, which is similar to my case. The third section is similar to my case, while the first and second case, I kept it here, to show that NDSolve[] solves the nested If[] with no problem. So you can directly go to the third section, please see the comments to go to the correct section. The reason I am posting it here, is even the Piecewise[] is not solving in my (original problem) case.
> 
> Please suggest me ways to solve this third case with nested If[]. Thank you.
> 
> Regards,
> Gopinath
> University of Oklahoma
> 
> (* code starts here *)
> 
> (* First section: Showing simple sine function inside NDSolve[] *)
> funReg[t_] := Sin[t];
> solReg = NDSolve[{y''[t] + y'[t] + y[t] - funReg[t] == 0, y[0] == 0, 
>     y'[0] == 1}, y, {t, 0, 1}];
> Plot[Evaluate[{y[t], y'[t]} /. solReg], {t, 0, 1}, 
>  PlotStyle -> {Black, {Red, Dashed}} ]
> (* Here no particular time value is required for the \
> function,i.e.Sin[t] is valid for any time t *)
> (* Second Section: Nested If[] inside NDSolve[] *)  
> funifcase1[t_] := 
>   If[0 <= t < 1/3, Sin[t], 
>    If[1/3 <= t <= 2/3, -1, If[2/3 < t <= 1, Cos[t]]]];
> Print["funifcase1 is given by ", funifcase1[t]];
> solifcase1 = 
>   NDSolve[{y''[t] + y'[t] + y[t] - funifcase1[t] == 0, y[0] == 0, 
>     y'[0] == 1}, y, {t, 0, 1}];
> Plot[Evaluate[{y[t], y'[t]} /. solifcase1], {t, 0, 1}, 
>  PlotStyle -> {Black, {Red, Dashed}}]
> (* In the above also, the function is undetermined (I mean, dependent \
> on time t, which is not supplied until the NDSolve[] increments from \
> initial conditions step by step by some direct integration scheme, I \
> guess *)
> (* Third case: I expect this case also to solve because it is very \
> similar to the above cases *) 
> sep = 1;
> len = 3;
> wdef1[t_] := y[t];
> wdef2[t_] := y[t];
> val1 = 50;
> val2 = 20;
> xv = 1/2;
> yv = 1/5;
> 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]];
> 
> 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],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}}]
> (* However the nested If[] does not solve, but the Piecewise[] does. \
> But both are same definitions and same set of equations inside of \
> NDSolve[]. And I expect similar behavior from NDSolve[] for these \
> cases *)
> 
> (* code ends here *)
> 


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