       Poisson-Boltzmann equation

• To: mathgroup at smc.vnet.net
• Subject: [mg107623] Poisson-Boltzmann equation
• From: michael partensky <partensky at gmail.com>
• Date: Sat, 20 Feb 2010 06:37:02 -0500 (EST)

```Does anybody know any Mathematica resources for solving non-linear
Poisson-Boltzmann equations for some simple geometries? I need a quick
answer (responding to a paper's referee)  and do not have time to get  into

Thanks
Michael

On Fri, Feb 19, 2010 at 3:35 AM, michael partensky <partensky at gmail.com>wrote:

>
> In   =   md[t] = Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]}]
> Out =  If[Re(t)<0,Sqrt[2 \[Pi]] E^(t^2/2) t
> (erf(t/Sqrt)+1)+2,Integrate[E^(t
> Sqrt[u]-u/2),{u,0,\[Infinity]},Assumptions->Re(t)>=0]]
> However,
> In =    md[t] - Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]},
>  Assumptions -> Re[t] < 0]
> Out = Sqrt[2 \[Pi]] E^(t^2/2) t (erf(t/Sqrt)+1)+2
> In =    md[t] - Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]},
>  Assumptions -> Re[t] > 0]
> Out = Sqrt[2 \[Pi]] E^(t^2/2) t (erf(t/Sqrt)+1)+2
>
> Why doesn't yellow output contain the same analytical expression  for both
> the assumptions (or just one analytical expression)?
> I thought that the original expression is returned only when the analytical
> result does not exist. What am I missing?
> Thanks. Michael.
>
>
>

```

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