Re: System of coupled PDE's initial value problem
- To: mathgroup at smc.vnet.net
- Subject: [mg38924] Re: System of coupled PDE's initial value problem
- From: "Sasha" <yashin at stanford.edu>
- Date: Mon, 20 Jan 2003 00:45:06 -0500 (EST)
- References: <b0dddl$i8h$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
just some numbers a=1,m=23,e=0.1,el=30; "Selwyn Hollis" <selwynh at earthlink.net> wrote in message news:b0dddl$i8h$1 at smc.vnet.net... > 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. > > > > > > > >