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Re: NDSolve with Boundary Condition

• To: mathgroup at smc.vnet.net
• Subject: [mg107780] Re: NDSolve with Boundary Condition
• From: marjan <marjan84 at gmail.com>
• Date: Thu, 25 Feb 2010 17:38:04 -0500 (EST)
• References: <201002231303.IAA16128@smc.vnet.net> <hm31vk$m5p$1@smc.vnet.net>

Dear  Patrick,

Thanks for your mail, the comment was useful.

another thing is that if I solve this equation in one dimension with
the real value of boundary conditions, after finding the best value
for Precisions :

ss = NDSolve[{D[Y[z], z, z] + 10^12 Sin[Y[z]] Cos[Y[z]] ==
   0, (D[Y[z], z] /. z -> 0) ==
   2*10^6, (D[Y[z], z] /. z -> 7*10^-6) == 2*10^6},
 Y[z], {z, 0, 7*10^-6}, WorkingPrecision -> 12, PrecisionGoal -> 7,
 Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 7},
 InterpolationOrder -> All]

It gives this error

NDSolve::berr:

There are significant errors {-796330.005638,-795426.001883} in the
boundary value residuals.  Returning the best solution found

{{Y[z] ->InterpolatingFunction[{{0,7.00000000000=D710^-6 }},<>][z]}}

should I be worried about this error or this is at least the best
approximation solution that is  given?

Regards

Marjan

On Feb 24, 12:19 pm, Patrick Scheibe <psche... at trm.uni-leipzig.de>
wrote:
> Hi,
>
> check
>
> D[f[x, y], x] // InputForm
>
> which gives
>
> Derivative[1, 0][f][x, y]
>
> Therefore, you can use something like
>
> Derivative[1, 0][f][0, y] == blub
>
> to give the values at the 0-boundary. If you want a working sample, read
> the NDSolve documentation carefully.
>
> Cheers
> Patrick
>
> On Tue, 2010-02-23 at 08:03 -0500, marjan wrote:
> > Dear MathGroup members,
>
> > Please help me with this:
> > I am trying to solve an numerical equation: sol = NDSolve[{D[Y[z, t],
> > z, z] +
> >      10^12 Sin[Y[z, t]] Cos[Y[z, t]] == D[Y[z, t], t]
> > with boundary conditions: d(Y[a, t])/dz = 2*10^6  and   d(Y[b, t]=
)/dz
> > = 2*10^6 , but i don't know how to write the boundary condition in
> > this equation. when I write it like D[Y[a, t], z] == 20*10^5, D[Y [=
b,
> > t], z] == 20*10^5 Mathematica gives this error
>
> > NDSolve::deqn: equation or list of equations expected instead of
> > "false" in the first argument {D[Y[z, t], z, z] +
> >      10^12 Sin[Y[z, t]] Cos[Y[z, t]] == D[Y[z, t], t] , False=
,False}
>
> > Thanks for your attention
> > Marjan

• References:
  • NDSolve with Boundary Condition
    • From: marjan <marjan84@gmail.com>