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: <email@example.com>
- 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