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

• To: mathgroup at smc.vnet.net
• Subject: [mg91403] Re: NDSolve[] with nested If[] and Piecewise[] usage:
• From: Gopinath Venkatesan <gopinathv at ou.edu>
• Date: Wed, 20 Aug 2008 04:05:01 -0400 (EDT)

```Hello Jean,

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 *)

```

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