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Meshless Methods and Their Numerical Properties
book

Meshless Methods and Their Numerical Properties

by Hua Li, Shantanu S. Mulay
February 2013
Intermediate to advanced content levelIntermediate to advanced
447 pages
14h 16m
English
CRC Press
Content preview from Meshless Methods and Their Numerical Properties
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 Figure5.1a. The rst-order wave equa-
tion
φ=φ
a
tx,,
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 coefcients 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
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Publisher Resources

ISBN: 9781466517462