
218 Meshless methods and their numerical properties
5.2.1.1 Central time and central space multistep scheme
In this scheme, three virtual nodes are considered over time and space
domains, respectively, as shown in Figure5.1a. The rst-order wave equa-
tion
a
in the discretised form is given as
φ
φ
φ
=
φ
φ
φ
−+
−
+
−+
−
+
aaa
xt
xt
xt
aa aa
xt
xt
xt
{}
(, )
(,)
(, )
{}
(,)
(,)
(,)
jj jj jj
ij
ij
ij
ii ii ii
ij
ij
ij
,1 ,,1
1
1
,1 ,,1
1
1
(5.1)
The weighting coefcients in Equation (5.1) are computed by the locally
applied DQ method, as explained in Chapter 3. The inverse Fourier trans-
form is employed in the resulting equation to get the character