Re: NDSolve issues with initial and boundary conditions (corrected characters)
- To: mathgroup at smc.vnet.net
- Subject: [mg119282] Re: NDSolve issues with initial and boundary conditions (corrected characters)
- From: "Kevin J. McCann" <kjm at KevinMcCann.com>
- Date: Sat, 28 May 2011 07:21:06 -0400 (EDT)
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:
>>>
>
>