Re: euler without d/dt? time-independent conservation law.
- From: "Lane Straatman" <invalid@xxxxxxxxxxx>
- Date: Mon, 5 Mar 2007 02:04:20 -0500
"Helmut Jarausch" <jarausch@xxxxxxxxxxxxxxxxxxx> wrote in message
news:54qj34F2237qnU1@xxxxxxxxxxxxxxxx
Phil Scadden wrote:I'm having trouble with the notation. Can you describe further what you
Looking to solve time-independent conservation law.snip
[f(u)]_x + [g(u)]_y =0
with initial condtions u(x_0(t),y_0(t))=u_0
and boundary conditions u(x_0),y) and u(x,y_0)
let's rewrite your equation to
(*) fp(u)*u_x + gp(u)*u_y=0 where fp(u) is the derivate of f at
u(x,y).
Now make the ansatz (characteristic) y= y(x), then
(**) d/dx (u(x,y(x))= u_x + u_y*yp where yp= d/dx y .
mean with "characteristic?" "Ansatz" makes more sense.
'u_x' I think wants to be "u sub x" but I can't divine what 'u_y*yp' might
be. Gruss, LS
.
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