
Re: System of differential equations
Posted:
Dec 7, 2012 1:37 AM


On 12/6/2012 3:56 AM, hazem.abdelhafiz@gmail.com wrote: > Dear all, > I want to solve this system of equations but I always get an error > > NDSolve::ndnum:Encountered nonnumerical value for a derivative at t==0 > > can any one help me on this > > s=NDSolve[{ > ph1''[t]+ph1'[t]+sin[ph1[t]]mu[t]mu'[t]==0.005, > ph2''[t]+ph2'[t]+sin[ph2[t]]+mu[t]+mu'[t]==0.005, > 0.2mu'[t]+mu[t]==ph1'[t]ph2'[t], > ph2[0]==0, > ph1[0]==0, > ph2'[0]==0, > ph1'[0]==0, > mu[0]==0 > }, > {ph1[t],ph2[t],mu[t]}, > {t,0,5000} > ] >
It is Sin[] not sin[]. Mathematica is Case Sensitive. It is better to write things in more lines than one so it is easier to read and modify.
 eq1 = ph1''[t] + ph1'[t] + Sin[ph1[t]]  mu[t]  mu'[t] == 0.005; eq2 = ph2''[t] + ph2'[t] + Sin[ph2[t]] + mu[t] + mu'[t] == 0.005; eq3 = 0.2 mu'[t] + mu[t] == ph1'[t]  ph2'[t]; ic = {ph2[0] == 0, ph1[0] == 0, ph2'[0] == 0, ph1'[0] == 0,mu[0] == 0}; s = NDSolve[Flatten@{eq1, eq2, eq3, ic}, {ph1[t], ph2[t], mu[t]}, {t, 0.01,5000}] 
{{ph1[t] > InterpolatingFunction[][t], ph2[t] > InterpolatingFunction[][t], mu[t] > InterpolatingFunction[][t]}}
From the warning messages I see, this looks like a stiff system, you might want to look into using options to handle this. see NDSolve documentation for more information on this.
Nasser

