An improved element-free Galerkin method for numerical modeling of the biological population problems

Engineering Analysis with Boundary Elements

Volumn 40, Issue , 2014, Pages 181-188

  Zhang, L W ^a,b   Deng, Y J ^b,c   Liew, K M ^b,d  

^a SHANGHAI OCEAN UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c SHANGHAI UNIVERSITY   (China)

^d Shenzhen Hi Tech Industrial Park ^*  (Hong Kong)

Author keywords

Biological population equation; Improved element free Galerkin method; Improved moving least square approximation

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINED OPTIMIZATION; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; POPULATION STATISTICS;

BIOLOGICAL POPULATIONS; CONVERGENT SOLUTIONS; DEGENERATE PARABOLIC EQUATION; ELEMENT FREE GALERKIN METHODS; ESSENTIAL BOUNDARY CONDITIONS; IMPROVED ELEMENT FREE GALERKIN (IEFG) METHODS; INITIAL AND BOUNDARY CONDITIONS; MOVING LEAST SQUARE APPROXIMATION;

COMPUTATIONAL MECHANICS;

EID: 84892962543     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2013.12.008     Document Type: Article

References (28)

1. ME Gurtin, and RC MacCamy On the diffusion of biological population Math Biosci 33 1977 35 49
2. DG Aronson The porous medium equation, lecture notes in mathematics 10 1985 Springer-Verlag Berlin
3. W Jager, and YG Lu Global regularity of solutions for general degenerate parabolic equations in 1-D J Differ Equ 140 1997 365 377 (Pubitemid 127340269)
4. YG Lu. Holder estimate of solutions of biological population equations Appl Math Lett 13 2000 123 126
5. L Giuggioli, and VM Kenkre Analytic solutions of a nonlinear convective equation in population dynamics Physica D 183 2003 245 259
6. WSC Gurney, and RM Nisbet The regulation of inhomogeneous populations J Theor Biol 52 1975 441 457
7. YG Lu H-order estimates of solutions of biological population equations Appl Math Lett 13 2000 123 126
8. T Belytschko, YY Lu, and L Gu Element-free Galerkin methods Int J Numer Methods Eng 37 1994 229 256
9. T Belytschko, Y Krongauz, and D Organ Meshless methods: an overview and recent developments Comput Meth Appl Mech Eng 139 1996 3 47 (Pubitemid 126382692)
10. RJ Cheng, and KM Liew The meshless method for two-dimensional unsteady heat conduction problems Comput Mech 45 2009 1 10
11. KM Liew, TY Ng, X Zhao, and JN Reddy Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells Comput Meth Appl Mech Eng 191 2002 4141 4157
12. KM Liew, HY Wu, and TY Ng Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis Comput Mech 28 2002 390 400 (Pubitemid 34715189)
13. KM Liew, YC Wu, GP Zou, and TY Ng Elasto-plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming Int J Numer Meth Eng 55 2002 669 683
14. KM Liew, XL Chen, and JN Reddy Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates Comput Meth Appl Mech Eng 193 2004 205 224 (Pubitemid 38086750)
15. JJ Monaghan An introduction to SPH Comput Phys Commun 48 1998 89 96
16. W Chen New RBF collocation methods and kernel RBF with applications Meshfree methods for partial differential equations 1 2000 Springer-Verlag 75 86
17. KM Liew, X Zhao, and TY Ng The element-free kp-Ritz method for vibration of laminated rotating cylindrical panels Int J Stab Dyn 2 2002 523 558
18. X Zhao, Q Li, KM Liew, and TY Ng The element-free kp-Ritz method for free vibration of conical shell panels J Sound Vib 295 2006 906 922 (Pubitemid 43903525)
19. X Zhao, YY Lee, and KM Liew Free vibration analysis of functionally graded plates using the element-free kp-Ritz method J Sound Vib 319 2009 918 939
20. X Zhao, and KM Liew Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method Comput Meth Appl Mech Eng 198 2009 2796 2811
21. SN Atluri, and T Zhu A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Comput Mech 22 1998 117 127 (Pubitemid 128620889)
22. WK Liu, S Jun, and YF Zhang Reproducing kernel particle methods Int J Numer Meth Eng 20 1995 1081 1106
23. Z Zhang, KM Liew, and YM Cheng Analyzing 2D fracture problems with the improved element-free Galerkin method Eng Anal Boundary Elem 32 2008 241 250
24. Z Zhang, P Zhao, and KM Liew Improved element-free Galerkin method for two-dimensional potential problems Eng Anal Boundary Elem 33 2009 547 554
25. Z Zhang, P Zhao, and KM Liew Analyzing three-dimensional potential problems with the improved element-free Galerkin method Comput Mech 44 2009 273 284
26. KM Liew, Y Cheng, and S Kitipornchai Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems Int J Numer Meth Eng 65 2006 1310 1332 (Pubitemid 43224818)
27. Z Zhang, DM Li, YM Cheng, and KM Liew The improved element-free Galerkin method for three-dimensional wave equation Acta Mech Sin 28 2012 808 818
28. RJ Cheng, and KM Liew Analyzing modified equal width (MEW) wave equation using the improved element-free Galerkin method Eng Anal Boundary Elem 36 2012 1322 1330