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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
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
kM
() () ()0 (1,, )
k
jj
kd
j
n
1
(3.75)
For the M
t
collocation points on the Neumann boundary,
==
=
xBu Butk M() () ()(1,2,, )
k
jj
k
t
j
n
1
(3.76)
For the M
u
collocation points on the Dirichlet boundary,
==
=
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 ...
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Publisher Resources

ISBN: 9781466517462