
238 Meshless methods and their numerical properties
where h and k are the spacings between the virtual nodes situated in the
space and time computation domains, respectively. The terms u ,
xxxx,
u
tt,
and u
ttt,
in Equation (5.53) represent the dispersion corresponding to the
space domain term u
xx,
and the dissipation and dispersion corresponding
to the term u
t,
in the time domain, respectively. The dissipation or damp-
ing in the time domain term is replaced as =α
tt xxxx,
2
,
by
x
.
As a result, Equation (5.53) is modied as
−α =
α
−
α
−
uu
h
u
k
u
k
u
12
txx xxxx xxxx ttt,,
2
,
2
,
2
,
(5.54)
In order to make the dispersion or os ...