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 *) >