
270 Meshless methods and their numerical properties
polynomial basis of function approximation. The governing equation and
boundary conditions are given as
df
dx
x
xx
x6
2
4exp (0 1)
2
222
=− −
α
−
−β
α
−
−β
α
(6.15)
fx
df x
dx
(0)exp ,
(1)
32
1
exp
1
2
2
== −
β
α
=
=− −
−β
α
−
−β
α
(6.16)
Table6.2 Convergence rates for rst 1-D problem of
Poisson equation by ARDQ method when
random eld nodes at beginning of
computation are combined with cosine and
uniform virtual nodes
Function
Convergence rate
(cosine virtual nodes)
Convergence rate
(uniform virtual nodes)
f 2.31 3.8
f
, x
1.32 1.1
f
, x x
0.4 0.5
Source: S.