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advection eq. + sine-Gordon eq.

• To: mathgroup at smc.vnet.net
• Subject: [mg13207] advection eq. + sine-Gordon eq.
• From: Ravi C Venkatesan <rcv_dac at giaspn01.vsnl.net.in>
• Date: Mon, 13 Jul 1998 07:42:56 -0400
• Sender: owner-wri-mathgroup at wolfram.com

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.... 
 
Thanx
 
Ravi