Re: How to use FindMaximum with a parameter passed to NDSolve??

*To*: mathgroup at smc.vnet.net*Subject*: [mg129146] Re: How to use FindMaximum with a parameter passed to NDSolve??*From*: Juan Barandiaran <barandiaran.juan at gmail.com>*Date*: Tue, 18 Dec 2012 02:37:05 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121217075827.C668D6947@smc.vnet.net> <CAEtRDSec3Cz0-Sas3+KVxYa+XAS0T4xtmhi5URa98HS5k5Yu0A@mail.gmail.com>

Thanks Bob, your answer solves my question: just by adding ?NumericQ to the function "pendulum" with NDSolve everything works fine apart from the precision problems which is another matter (not important in this case). pendulum[long_?NumericQ] := First[fi /. NDSolve[{fi''[t] + 9.8 Cos[long] Sin[fi[t]] + .5 fi'[t] == 0, fi[0] == Pi/2, fi'[0] == 0}, fi, {t, 0, 50}]] total[dynamics_, p_] := dynamics[3.1] + p FindMaximum[total[pendulum[long], long ] , {long, 0.01}] But why? What is the rationale behind it? If I understand correctly, using ?NumericQ in the variables of a function should test the variable and only execute the function if the variable is a number. Is this test enough for the FindMaximum function to assign a value to the long before calling total, and then pendulum, and then NDSolve? Why? Thanks a lot for your answer, it helped me a lot. Best regards, JBB 2012/12/17 Bob Hanlon <hanlonr357 at gmail.com> > Since pendulum uses NDSolve it can only be evaluated for a numeric > argument; consequently, its definition should be restricted to numeric > arguments. You will also need to use a higher precision than machine > precision. > > eqns = Rationalize[{ > fi''[t] + 9.8 Cos[long] Sin[fi[t]] + > .5 fi'[t] == 0, fi[0] == Pi/2, fi'[0] == 0}, 0]; > > pendulum[long_?NumericQ] := First[fi /. NDSolve[ > eqns, fi, {t, 0, 50}, WorkingPrecision -> 25]] > > total[dynamics_, p_] := dynamics[31/10] + p > > max = FindMaximum[{total[pendulum[long], long]}, > {long, 0.01`30}, WorkingPrecision -> 30]; > > max /. x_?NumericQ :> Round[x, 10.^-6] > > {13.3595, {long -> 9.81034}} > > > Bob Hanlon > > > On Mon, Dec 17, 2012 at 2:58 AM, JBB <barandiaran.juan at gmail.com> wrote: > > Hello, > > > > This is probably a simple sintax question, but could somebody tell me > how can I use the FindMaximum function when the variable used has to be > used in an internal NDSolve?? > > > > A simplified version of some code to show the error is as follows: > > > > pendulum[long_] := > > First[fi /. > > NDSolve[{fi''[t] + 9.8 Cos[long] Sin[fi[t]] + .5 fi'[t] == 0, > > fi[0] == Pi/2, fi'[0] == 0}, fi, {t, 0, 50}]] > > > > total[dynamics_, p_] := dynamics[3.1] + p > > > > FindMaximum[{total[pendulum[long], long ] }, {long, 0.01}] > > > > I get the following error: > > > > In[146]:= FindMaximum[ > > Evaluate[total[pendulum[long], long ] ], {long, 0.01}] > > > > During evaluation of In[146]:= NDSolve::ndnum: Encountered non-numerical > value for a derivative at t == 0.`. >> > > > > During evaluation of In[146]:= ReplaceAll::reps: {NDSolve[{9.8 Cos[long] > Sin[fi[<<1>>]]+0.5 > (fi^\[Prime])[t]+(fi^\[Prime]\[Prime])[t]==0,fi[0]==\[Pi]/2,(fi^\[Prime])[0]==0},fi,{t,0,50}]} > is neither a list of replacement rules nor a valid dispatch table, and so > cannot be used for replacing. >> > > > > During evaluation of In[146]:= FindMaximum::nrnum: The function value > -0.01-fi[3.1] is not a real number at {long} = {0.01}. >> > > > > Out[146]= FindMaximum[long + fi[3.1], {long, 0.01}] > > > > If I understand correctly, probably because the variable "long" has not > been assigned a value by FindMaximum before calling the internal NDSolve. > > > > Is there a simple way of doing this? > > In my real case the functions are longer but the essence of the problem > is the same: I have to find the maximum of some function in which the > variables are parameters of other functions including a NDSolve. > > > > Thanks for any hint, > > > > JBB

**References**:**How to use FindMaximum with a parameter passed to NDSolve??***From:*JBB <barandiaran.juan@gmail.com>