
310 Meshless methods and their numerical properties
where L is a differential operator and f(x,y) an unknown real function. By
the point collocation technique and taking
y(,
as the approximation of
f(x,y), the problem is discretised and expressed approximately by
Lf xy Px y(,)(
ii
= i = 1,2,…, NΩ (7.6)
fx yQxy(,)(
ii
=
i = 1,2,…, N
D
(7.7)
fx y
Rxy
(,)
(,)
ii
∂
= i = 1,2,…, N
N
(7.8)
where N
Ω
, N
D
, and N
N
are the numbers of scattered points in the interior
domain and along the Dirichlet and Neumann boundary edges, respec-
tively. The total number of scattered points is thus N
T
= (N
Ω
+ N
D
+ N
N
).
Approximating Equations (7.6) to (7.8