
228 Meshless methods and their numerical properties
0.8
0.6
0.4
0.2
–0.2
–0.4
–0.6
–0.8
–1
0 0.2 0.4
(a) (b)
0.6
x
0.8
t = 0
t = 0.5
t = 1.0
t = 0.25
t = 0.75
t = 0
t = 0.5
t = 1.0
t = 0.0
t = 0.4
t = 0.6
t = 0.25
t = 0.75
1
0
–5
–4
–3
–2
–1
0
1
2
3
4
5
0.2 0.4 0.6
Oscillations
x
0.8 1
0
0.8
0.6
0.4
0.2
–0.2
–0.4
–0.6
–0.8
–1
0 0.2 0.4 0.6
x
0.8
0
φ
φ
Figure 5.6 The wave is preserved for r = 1 (a) and r = 0.5 (b), but oscillations are observed
for r = 2 (c) when the rst-order wave equation is solved by locally applied
DQ method with the rst discretisation scheme. (From H. Li, S. Mulay, and
S. See. (2009c). Computer Modeling in Engineering and Sciences, 54, 147–199.
With permission.)
0.8
0.6 ...