Re: NDSolve and "periodic" boundary conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg124020] Re: NDSolve and "periodic" boundary conditions
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Fri, 6 Jan 2012 04:13:56 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201051057.FAA14700@smc.vnet.net>

```
On Thu, 5 Jan 2012, gac wrote:

> Can NDSolve use a "periodic" boundary condition something like:
>
>     f[0] = f[1]+1      (I know it's not actually periodic)
>
> Even better, since I want to solve a PDE, something like:
>
>     f[0,t] = f[1,t] + I Exp[I t]
>
> I can't get around this error:
>
>     NDSolve::bcedge: Boundary condition... is not     specified on a single edge of the boundary of the computational domain. >>
>
> I'm trying to solve Eq. (8) of Bowers' and Moody's "Cavity equations for a laser with an injected signal," J. Opt. Soc. Am. B 11:2266 (1994).  The boundary condition is the reflected cavity field (periodic) plus the portion of the injected field transmitted into the cavity through the output mirror.
>
> Thanks very much.
>
> GAC
>
>

>From the documetation

NDSolve[{Derivative[2, 0][u][t, x] == Derivative[0, 2][u][t, x],
u[0, x] == E^(-x^2), Derivative[1, 0][u][0, x] == 0,
u[t, -10] == u[t, 10]}, u, {t, 0, 40}, {x, -10, 10}]

Hope this helps,
Oliver

```

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