LUO Han-Zhong;LIU Wue-Wen;HUANG Xing-Chun . Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics[J]. Applied Mathematics and Mechanics, 2011 , 32(6) : 777 -788 . DOI: 10.1007/s10483-011-1457-6

[1] Gingold, R. A. and Monaghan, J. J. Smoothed particle hydrodynamics: theory and application
to nonspherical stars. Royal Astronomical Society, Monthly Notices, 181, 375–389 (1977)

[2] Nayroles, B., Touzot, G., and Villon, P. Generalizing the finite element method: diffuse approximation
and diffuse elements. Computational Mechanics, 10(5), 307–318 (1992)

[3] Belytschko, T., Lu, Y. Y., and Gu, L. Element-free Galerkin methods. International Journal for
Numerical Methods in Engineering, 37(2), 229–256 (1994)

[4] Melenk, J. M. and Babuska, I. The partition of unity finite element method: basic theory and
applications. Computer Methods in Applied Mechanics and Engineering, 139(1-4), 289–314 (1996)

[5] Duarte, C. A. and Oden, J. T. An h-p adaptive method using clouds. Computer Methods in
Applied Mechanics and Engineering, 139(1-4), 237–262 (1996)

[6] Liu, W. K., Jun, S., and Zhang, Y. F. Reproducing kernel particle methods. International Journal
for Numerical Methods in Fluids, 20(8-9), 1081–1106 (1995)

[7] Chen, J. S., Pan, C. H., Wu, C. T., and Liu, W. K. Reproducing kernel particle methods for
large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and
Engineering, 139(1-4), 195–227 (1996)

[8] Sukumar, N., Moran, B., and Belytschko, T. The natural element method in solid mechanics.
International Journal for Numerical Methods in Engineering, 43(5), 839–887 (1998)

[9] Atluri, S. N. and Zhu, T. L. The meshless local Petrov-Galerkin (MLPG) approach for solving
problems in elasto-statics. Computational Mechanics, 25(2-3), 169–179 (2000)

[10] Kansa, E. J. Multiqudrics — a scattered data approximation scheme with applications to computational
fluid-dynamics — I. surface approximations and partial derivatives. Computers and
Mathematics with Applications, 19(8-9), 127–145 (1990)

[11] Kansa, E. J. Multiqudrics — a scattered data approximation scheme with applications to computational
fluid-dynamics — II. solutions to parabolic, hyperbolic and elliptic partial differential
equations. Computers and Mathematics with Applications, 19(8-9), 147–161 (1990)

[12] Zhang, X., Chen, J. S., and Osher, S. A multiple level set method for modeling grain boundary
evolution of polycrystalline materials. Interaction and Multiscale Mechanics, 1, 178–191 (2008)

[13] Belytschko, T., Kronggaus, Y., Organ, D., and Fleming, M. Meshless methods: an overview and
recent developments. Computer Methods in Applied Mechanics and Engineering, 139(1-4), 3–47
(1996)

[14] Zhang, X., Liu, Y., and Ma, S. Meshfree methods and their applications (in Chinese). Advances
in Mechanics, 39(1), 1–36 (2009)

[15] Liu, G. R. Meshfree Methods: Moving Beyond the Finite Element Method, 2nd ed., CRC Press
(2009)

[16] Zhang, X., Song, K. Z., Lu, M. W., and Liu, X. Meshless methods based on collocation with radial
basis function. Computational Mechanics, 26(4), 333–343 (2000)

[17] Huang, J., Zhang, J., and Chen, G. G. Stability of Schr¨odinger-Poisson type equations. Applied
Mathematics and Mechanics (English Edition), 30(17), 1469–1474 (2009) DOI 10.1007/s10483-
009-1113-y

[18] Ye, Z. A new finite element formulation for planar elastic deformation. International Journal for
Numerical Methods in Engineering, 40(20), 2579–2591 (1997)

[19] Zhu, H. H., Yang, B. H., Cai, Y. C., and Xu, B. Application of meshless natural element method
to elastoplastic analysis (in Chinese). Rock and Soil Mechanics, 25(4), 671–674 (2004)

[20] Xiong, Y. B. and Long, S. Y. An analysis of plates on the winkler foundation with the meshless
local Petrov-Galerkin method (in Chinese). Journal of Hunan University (Natural Science), 31(4),
101–105 (2004)

[21] Li, S. C. and Chen, Y. M. Meshless numerical manifold method based on unit partition (in
Chinese). Acta Mechanica Sinica, 36(4), 496–500 (2004)

[22] Hu, H. Y., Chen, J. S., and Hu, W. Error analysis of collocation method based on reproducing
kernel approximation. Numerical Methods for Partial Differential Equations, 27(3), 554–580
(2009)

[23] Hu, H. Y., Lai, C. K., and Chen, J. S. A study on convergence and complexity of reproducing
kernel particle method. Interaction and Multiscale Mechanics, 2, 295–319 (2009)

[
[24] Lucy, L. A numerical approach to testing the fission hypothesis. The Astronomical Journal, 82(18),
1013–1024 (1977)

[25] Monoghan, J. J. Why particle methods work. SIAM Journal on Scientific and Statistical Computing,
3(4), 422–433 (1982)

[26] Monoghan, J. J. An introduction to SPH. Computer Physics Communications, 48(1), 89–96 (1988)

[27] Randles, P. W. and Libersky, L. D. Smoothed particle hydrodynamics: some recent improvements
and applications. Computer Methods in Applied Mechanics and Engineering, 139(1-4), 375–408
(1996)

[28] Liu, W. K., Jun, S., Li, S., Adee, J., and Belytschko, B. Reproducing kernel particle methods
for structural dynamics. International Journal for Numerical Methods in Engineering, 38(10),
1655–1679 (1995)

[29] Liu, W. K. and Chen, Y. Wavelet and multiple scale reproducing kernel particle methods. International
Journal for Numerical Methods in Fluids, 21(16), 901–931 (1995)

[30] Chen, J. S., Pan, C., Roque, M. O. L., and Wang, H. P. A Lagrangian reproducing kernel particle
method for metal forming analysis. Computational Mechanics, 22(3), 289–307 (1998)

[31] Luo, H. Z., Chen, J. S., Hu, H. Y., and Huang, X. C. Stability of radial basis collocation method
for transient dynamics. Journal of Shanghai Jiaotong University (English Edition), 15(5), 615–621
(2010) DOI 10.1007/s12204-010-1057-4