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From: marjan on 23 Feb 2010 08:03
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



From: Patrick Scheibe on 24 Feb 2010 06:19
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
>
>
>


From: dh on 25 Feb 2010 01:49
Hi Marjan,
to make life easier, try to scale your variables that you get reasonable
numerical coefficients.
Then besides border condition, you also need initial values.
Note also, that a and b must have numerical values.
Partial derivatives at a certain place cane be specified in two ways,
either:
Derivative[1,0][Y][0,t]
or:
(D[Y[z,t],z]/.z->0)
here is an example:

eq = {D[Y[z, t], z, z] + Sin[Y[z, t]] Cos[Y[z, t]] == D[Y[z, t], t],
Derivative[1, 0][Y][0, t] == 1,
Derivative[1, 0][Y][1, t] == 1,
Y[z, 0] == Sin[2 Pi z]/(2 Pi)};
sol = Y[z, t] /. NDSolve[eq, Y[z, t], {z, 0, 1}, {t, 0, .1}][[1]]
ContourPlot[sol, {z, 0, 1}, {t, 0, .1}]

Daniel

On 23.02.2010 14:03, 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
>
>
>


--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh(a)metrohm.com>
Internet:<http://www.metrohm.com>


From: marjan on 25 Feb 2010 17:36
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...(a)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


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