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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
Stability analyses 223
The weighting coefcients from Equation (5.20) are computed by the
locally applied DQ method, and the characteristic polynomial (Appendix
A) is given as
φ=−+−α
zz
zi
() 43
()
2
(5.21)
where γ = cos(θ) − 2,
α= γ
r2[1cos() ] , and β = 2rsin(θ)γ. The complex
conjugate polynomial of Equation (5.21) is given as
φ=−+−αzz iz() 14 (3 )
*2
(5.22)
The conditions
φ=
|(0)
|1
*
and φ=−α−βi(0)3 are obtained from
Equations (5.21) and (5.22). For Equation (5.21) to be the VN polynomial,
φ−
φ≥[|
(0)| |(0)|] 0
*2 2
results in (Miller, 1971)
−−α−β≥1(3) 0
22
(5.23)
It is difcult to analytically solve Equation (5.23). Therefore the roots of
ϕ
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Publisher Resources

ISBN: 9781466517462