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

*To*: mathgroup at smc.vnet.net*Subject*: [mg119392] Re: NDSolve issues with initial and boundary conditions (corrected characters)*From*: Oliver Ruebenkoenig <ruebenko at wolfram.com>*Date*: Wed, 1 Jun 2011 06:54:49 -0400 (EDT)

On Wed, 1 Jun 2011, Arturo Amador wrote: Arturo, > 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. The shooting method is implemented. tutorial/NDSolveBVP#659822336 There are some options for starting initial conditions, perhaps those are useful. Oliver > 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: >>>>> >>> >>> >> > >