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Re: advection eq. + sine-Gordon eq.

• To: mathgroup at smc.vnet.net
• Subject: [mg13264] Re: advection eq. + sine-Gordon eq.
• From: Robert Knapp <rknapp>
• Date: Fri, 17 Jul 1998 03:17:55 -0400
• Organization: Wolfram Research, Inc.
• References: <6od1nu$hm8@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Ravi C Venkatesan wrote:
> 
> Hi,
> 
> Could someone please help me obtain/locate a Mathematica notebook
> (preferably V 2.2) that solves the advection equation and the
> sine-Gordon eq. using finite-differencing.
> 
> The advection eq. (sometimes called the linear convection eq.) is often
> found in fluid dynamics.  It is of the form u_t + a*u_x=0, where "a" is
> a constant.  The sine-Gordon eq. is of the form u_xx - u_tt = sin u.
> Here "x" and "t" are space and time, and u is the dependent variable.
> Also, for example, u_x = partial derivative of "u" with respect to "x",
> etc....
> 

Since the functionality was not built into Mathematica until 3.0, I
doubt you will find any good 2.2 or earlier examples.  

In any case, the third edition of The Mathematica Book shows an example
of a solution of the Sine-Gordon equation by NDSolve on p894. The
advection equataion can similrly be solved by NDSolve.

Rob Knapp
WRI