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