Student Support Forum: 'Data Fitting to Differential Equations' topicStudent Support Forum > General > "Data Fitting to Differential Equations"

 < Previous Comment | Next Comment > Help | Reply To Comment | Reply To Topic
 Author Comment/Response FRanc Solina Gilbert 10/05/05 4:48pm Hi yehuda :), Thanks for the advices -:). I start understanding Mathematica. I have found a posible solution to my problem. Since g[t] is my system's input (vibration initiator) and I replace g[t] by an Mathematica interpolated polynomial of the kind \!\(HSE[a_?NumberQ, b_?NumberQ, c_?NumberQ, d_?NumberQ] := Block[{sol, f}, sol = \(NDSolve[{\((a + b\ Abs[f[t]] + c\ f[t]\^2 + d\ Abs[f[t]\^3])\)\ f[ t] + c\ \(f'\)[ t] == \(-0.2200821389305352`\) + 2.6933892154486747`\ t - 2.898740511629984`\ t\^2 + 1.4915822724657741`\ t\^3\ , f[0] == 0}, f, {t, 0, 500}, Method -> "\"]\)[\([1]\)]; Plus @@ Apply[\((f[#1] - #2)\)^2 &, data, { 1}] /. sol]; NMinimize[HSE[A, B, C, D], {A, B, C, D}, \ Method -> "\"]\) then I get after some error massages a solution to my problem. Mathematica does a least square fit of the parameters (a,b,c,d). Now, lets come to the error massages: NDSolve::ndcf. Repeated convergence test failure at t == 123.06374629313223; unable to continue. NDSolve::ndsz: At t == 18.585850047911073`, step size is effectively zero; singularity or stiff system suspected I assume that the singularity in my system result from a polynomial attempt. Because, when I replace the right side of the equation with, a periodic attempt of the kind Sin[t]+(Sin[t])^2, then Mathematica finds automatically a least square fit to my problem. Now the system is not singular anymore. Normally Mathematica tries a polynomial interpolation. I would like to use a Fourier interpolation. I concentrate myself at the moment to periodic input signals. So a Fourier analysis is something to thing about. Is there a possibility to do that with the aim to get a peridical interpolation function for g[t]? Regards, Franc URL: ,

 Subject (listing for 'Data Fitting to Differential Equations') Author Date Posted Data Fitting to Differential Equations Dr. Frank So... 09/28/05 6:01pm Re: Data Fitting to Differential Equations yehuda ben-s... 09/30/05 00:25am Re: Data Fitting to Differential Equations Frank Solina... 09/30/05 4:12pm Re: Data Fitting to Differential Equations Frank Solina... 10/01/05 08:26am Re: Data Fitting to Differential Equations yehuda ben-s... 10/02/05 2:20pm Re: Data Fitting to Differential Equations FRanc Solina... 10/05/05 4:48pm Re: Data Fitting to Differential Equations Franc Solina... 10/13/05 09:12am
 < Previous Comment | Next Comment > Help | Reply To Comment | Reply To Topic