
78 Meshless methods and their numerical properties
3.3.1.3 Direct collocation (DC) method
By substituting Equation (3.74) into Equations (3.70) to (3.72), we can have
a system of equations for the direct collocation method as follows. For the
M
d
internal collocation points,
…
∑
+= φ+ ==
=
xAu qAuq
() () ()0 (1,, )
k
jj
j
n
1
(3.75)
For the M
t
collocation points on the Neumann boundary,
…
∑
=φ==
=
xBu Butk M() () ()(1,2,, )
k
jj
k
t
j
n
1
(3.76)
For the M
u
collocation points on the Dirichlet boundary,
…
∑
=φ
=
xxuuukM() () (1,2,, )
k
jj
k
j
n
u
1
(3.77)
By the assembly of Equations (3.75) to (3.77), we can obtain the following
system of equations
KU = F (3.78)
The di ...