Re: Calculations with Interpolating Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg88526] Re: Calculations with Interpolating Functions*From*: oshaughn <oshaughn at northwestern.edu>*Date*: Wed, 7 May 2008 07:09:42 -0400 (EDT)*References*: <fvpcqn$mhn$1@smc.vnet.net>

On May 6, 6:44 am, Jo=E3o Paulo Casquilho <j... at fct.unl.pt> wrote: > Hi > > I obtain an Interpolating function as a solution of a differential equation > with the command NDSolve, lets call it =93solution=94, which gives x(t). Next I Your solution is of form solution = {x->InterpolatingFunction[...]} The expression 'Integrate' performs a *symbolic, exact* integral, which can be done on interpolating functions since their form is known. It cannot be done in general. So try this: xSol[t_] := (x[t]/.solution) NIntegrate[ Sin[xSol[t]], {t,0, tmax}]; > want to use this solution for further calculations. With the commands > =93result=Evaluate[x(t)/. First[solution]]=94 or =93result= x(t)/.solution, > {t,0,tmax}=94 I do the plot x(t) without any problems. Now, with version 5.2 I > manage to integrate x(t) or linear functions of it. But when I try to > integrate non linear functions of x(t), like x(t)^2 or Sin[x(t)] (which is > what I want), Mathematica is unable to give a numerical result, all I get > is an integral saying that there is an InterpolatingFunction in the > integrand. With Mathematica 6 the linear integration does not work either. > > Any help would be appreciated. > > Best Regards > > Joao Paulo