Re: NDSolve issues with initial and boundary conditions (corrected characters)

*To*: mathgroup at smc.vnet.net*Subject*: [mg119381] Re: NDSolve issues with initial and boundary conditions (corrected characters)*From*: Arturo Amador <arturo.amador at ntnu.no>*Date*: Wed, 1 Jun 2011 04:33:58 -0400 (EDT)

Ok, I wasn't expecting that. The system is supposed to have a solution for which h[L] == 0 is satisfied. Maybe there is something wrong with the approximation I am using. I would like to know how is that you can implement the shooting method. I will write a more complete post with the approximation I am using and some other methods I am using to solve the problem for which I am getting of course more issues. Is the bad thing of not being an expert in Mathematica : / -- Arturo Amador Cruz On May 28, 2011, at 1:21 PM, Kevin J. McCann wrote: > Arturo, > > I looked into your problem a bit more. NDSolve should be able to solve > BVP's, but I tried a shooting method instead with the condition h[0]==0, > replaced with h[L]==alpha, and I varied alpha a bit to see if I could > find a solution for which h[0]=0. I couldn't. I found a minimum, but it > was not close to zero. Is it possible that your problem does not have a > solution for the conditions you stated? I don't know what the physics of > the problem is. > > Kevin > > On 5/25/2011 7:31 PM, Arturo Amador wrote: >> I am sorry, here is the message without the In[] Out[] labels and with >> the missing definitions: >> >> Hi, >> >> Sorry for the previous message, it had some weird characters I have >> corrected it and resend it. >> >> I am having some issues when trying to solve a system of three coupled >> differential equations numerically using NDSolve. I am trying to specify >> boundary conditions for two of the variables in the same point (point at >> L) and a boundary condition for the last variable at zero. The >> mathematica code is: >> >> >> vd[x_]:=1/(2^(x+1) \[Pi]^(x/2) Gamma[x/2]) ; >> factorp[t_]:=(- 2 (Lambda Exp[t])^5 vd[3])/(3 * 8 g[t]^2); >> factorg[t_]:= (2 (Lambda Exp[t])^5 vd[3])/3; >> factorh[t_]:=-((2 (Lambda Exp[t])^5 vd[3])/3 ); >> >> vacuumlinearrhsp = (-((4 E^(-4 t) Sqrt[E^(2 t) Lambda^2] (-1 + n) g[t]^2)/ Lambda^4) - (12 g[t]^2)/(E^(2 t) Lambda^2 + 16 g[t]^2 p0[t])^(3/2)) factorp[t] >> >> vacuumcuadraticrhsg = ((24 E^(-6 t) Sqrt[E^(2 t) Lambda^2] (-1 + n) g[t]^4)/Lambda^6 + (216 g[t]^4)/(E^(2 t) Lambda^2 + 16 g[t]^2 p0[t])^(5/2)) factorg[t] >> >> vacuumcubicrhsh =(-((160 E^(-8 t) Sqrt[E^(2 t) Lambda^2] (-1 + n) g[t]^6)/Lambda^8) - (4320 g[t]^6)/(E^(2 t) Lambda^2 + 16 g[t]^2 p0[t])^(7/2)) factorh[t] >> >> (*Declarations*) >> Lambda = Sqrt[5] msig; >> >> L = -17090/10000; >> msig = 400; >> >> mp = 0; >> fp = 93; >> >> lambda = 2 (msig^2 - mp^2)/fp^2; >> gk0 = (lambda/24)^(1/2); >> pk0 = 1/2 fp^2; >> >> n = 4; >> >> >> sol = NDSolve[{D[p0[t], t] == vacuumlinearrhsp, 4 D[g[t]^2, t] + 3 h[t] D[p0[t], t] == vacuumcuadraticrhsg, D[h[t], t] == vacuumcubicrhsh, p0[L] == pk0, g[L]^2 == gk0^2, h[0] == 0}, {p0, g, h}, {t, L, 0}, Method -> {StiffnessSwitching, Method -> {ExplicitRungeKutta, Automatic}}]; >> >> with output: >> >> Power::infy: Infinite expression 1/0. encountered.>> >> >> Infinity::indet: Indeterminate expression (0. Sqrt[5] ComplexInfinity)/\[Pi]^2 encountered.>> >> >> Power::infy: Infinite expression 1/0.^2 encountered.>> >> >> Infinity::indet: Indeterminate expression (0. Sqrt[5] ComplexInfinity)/\[Pi]^2 encountered.>> >> >> Power::infy: Infinite expression 1/0. encountered.>> >> >> General::stop: Further output of Power::infy will be suppressed during this calculation.>> >> Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered.>> >> General::stop: Further output of Infinity::indet will be suppressed during this calculation.>> >> NDSolve::ndnum: Encountered non-numerical value for a derivative at t = -1.709.>> >> >> I am sure there is no singularity. I am getting this output no matter >> what value I am giving for h[0], as long as I specify the boundary >> condition in a point that is not L, it gives me this same error message. >> I have tried h[0.9L] and still the same. When h[t]=0 The system >> reduces to this: >> >> sol = NDSolve[{D[p0[t], t] == (Lambda Exp[t])^5/(24 Pi^2) ( (n - 1)/(Lambda Exp[t])^3 +3/((Lambda Exp[t])^2 + 16 p0[t] g[t]^2)^(3/2)), D[g[t]^2,t] == ((Lambda Exp[t])^5 * g[t]^4 )/(2 Pi^2) ((n - 1)/(Lambda Exp[t])^5 + 9/((Lambda Exp[t])^2 + 16 p0[t] g[t]^2)^(5/2)), p0[L] == pk0, g[L]^2 == gk0^2}, {p0, g}, {t, L, 0}, Method -> {StiffnessSwitching, Method - {ExplicitRungeKutta, Automatic}}]; >> >> For which I get nice solutions. >> >> >> >> Thanks in advance >> >> >> >> >>> You have functions factorp[t], factorg[t], and factorh[t] in your code without definitions. >>> >>> It would be a lot easier for us to cut and paste your stuff if you left off the In[] Out[] labels. >>> >>> Kevin >>> On 5/25/2011 6:59 AM, Arturo Amador wrote: >>>> Hi, >>>> >>>> Sorry for the previous message, it had some weird characters I have >>>> corrected it and resend it. >>>> >>>> I am having some issues when trying to solve a system of three coupled >>>> differential equations numerically using NDSolve. I am trying to specify >>>> boundary conditions for two of the variables in the same point (point at >>>> L) and a boundary condition for the last variable at zero. The >>>> mathematica code is: >>>> >> >> >