Re: System of coupled PDE's initial value problem
- To: mathgroup at smc.vnet.net
- Subject: [mg38917] Re: [mg38893] System of coupled PDE's initial value problem
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sun, 19 Jan 2003 00:33:01 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Alexander,
In your definition of p and p1, there are parameters a and m, which you
haven't specified. What should those be?
---
Selwyn Hollis
On Friday, January 17, 2003, at 05:39 AM, Alexander Yashin wrote:
> Hello,
>
> I am trying to solve system of 3 coupled PDE's but getting error
> NDSolve::"ndnum": "Encountered non-numerical value for a derivative at
> t==0"
> apparentely the problem is in inital conditions (derivate of one
> function
> that go into the equation
> for another is not specified explicitely in the initial moment of time)
> any que how to go around this would be greatly appreciated
>
> best regards
> alexander
>
> following system of 3 PDE
>
> eq11 = D[a0[t,x], {t, 2}] - D[a0[t, x], {x, 2}] == I*e*(Conjugate[f[t,
> x]]*D[f[t, x], {t, 1}] - f[t, x]*Conjugate[D[f[t, x], {t, 1}]]) +
> e^2*(a0[t,
> x] + el*x)*(Abs[f[t, x]])^2;
> eq12 = D[ax[t, x], {t, 2}] - D[ax[t, x], {x, 2}] ==I*e*(Conjugate[f[t,
> x]]*D[f[t, x], {x, 1}] - f[t, x]*Conjugate[D[f[t, x], {x, 1}]])
> +e^2*(ax[t,
> x] - el*t)*(Abs[f[t, x]])^2;
> eq13 = D[f[t, x], {t, 2}] - D[f[t, x], {x, 2}] + (m^2 - e^2*((a0[t, x]
> +
> el*x)^2))*f[t, x] -2*I*e*((a0[t, x])*D[f[t, x], {t, 1}]) == 0;
>
> with the initial and boundary conditions
>
> eq21 = a0[0, x] == 0; eq22 = Derivative[1, 0][a0][0, x] == 0; eq23 =
> a0[t, -x0] == 0; eq24 = a0[t, x0] == 0;
> eq31 = ax[0, x] == 0; eq32 = Derivative[1, 0][ax][0, x] == 0; eq33 =
> ax[t, -x0] == 0; eq34 = ax[t, x0] == 0;
> eq41 = f[0, x] == p; eq42 = Derivative[1, 0][f][0, x] == p1; eq43 =
> f[t, -x0] == 0; eq44 = f[t, x0] == 0;
>
> where
>
> p = NIntegrate[Exp[I*k*x - k^2/2*a^2], {k, 0, Infinity}];
> p1 = NIntegrate[-I*Sqrt[m^2 + k^2]*Exp[I*k*x - k^2/2*a^2], {k, 0,
> Infinity}];
>
> when I try to solve it numerically with
>
> res = NDSolve[{eq11, eq12, eq13, eq21, eq22, eq23, eq24, eq31, eq32,
> eq33,
> eq34, eq41, eq42, eq43, eq44},{a0[t, x], ax[t, x], f[t, x]}, {t, 0,
> 10},
> {x, -x0, x0}, StartingStepSize -> 0.03, MaxSteps -> 4000];
>
> it gives me
> NDSolve::"ndnum": "Encountered non-numerical value for a derivative at
> t==0"
> and quits
>
> i nailed it down to presence of D[f[t, x], {x, 1}] derivative in eq12
> equation which was not specified at t==0 in the initial conditions
> explicitly
> but should be known because f[0,x] is specified.
>
>
>