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advection eq. + sine-Gordon eq.
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