Re: euler without d/dt? time-independent conservation law.

Lane Straatman wrote:
"Helmut Jarausch" <jarausch@xxxxxxxxxxxxxxxxxxx> wrote in message news:54qj34F2237qnU1@xxxxxxxxxxxxxxxx
Phil Scadden wrote:
Looking to solve time-independent conservation law.
[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)

snip
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 .
I'm having trouble with the notation. Can you describe further what you mean with "characteristic?" "Ansatz" makes more sense.

Characteristic curves (that's a technical term) are curves on which the
solution is constant or given by the solution of an ordinary differential
equation.


'u_x' I think wants to be "u sub x" but I can't divine what 'u_y*yp' might be. Gruss, LS

u_x and u_y denote the partial derivative w.r.t. x (y, resp.).
The characteristic curve is assumed to have the form (x,y(x)); here yp is
an abbreviation for the derivative of that y(x) w.r.t. x (x being a scalar
variable).





--
Helmut Jarausch

Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany
.