Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method

Chinese Physics B

Volumn 21, Issue 10, 2012, Pages

  Cheng, Rong Jun ^a   Ge, Hong Xia ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b NINGBO UNIVERSITY   (China)

Author keywords

equal width (EW) wave equation; mesh free kp Ritz method; meshless method; solitary wave

Indexed keywords

DISPLACEMENT FIELD; ENERGY EXPRESSION; EQUAL WIDTH WAVE EQUATIONS; MESH-LESS METHODS; MESHFREE; NUMERICAL EXAMPLE; REPRODUCING KERNEL; RITZ METHODS; SYSTEM OF DISCRETE EQUATION;

COMPUTATIONAL MECHANICS; NONLINEAR ANALYSIS; SOLITONS;

WAVE EQUATIONS;

EID: 84867291392     PISSN: 16741056     EISSN: None     Source Type: Journal    
DOI: 10.1088/1674-1056/21/10/100209     Document Type: Article

References (57)

1. Donea J and Giuliani S 1974 Nucl. Eng. Des. 30 205
2. Bathe K J and Khoshgoftaar M R 1979 Nucl. Eng. Des. 51 389
3. Skerget P and Alujevic A 1983 Nucl. Eng. Des. 76 47 (Pubitemid 14506975)
4. Belytschko T, Krongauz Y and Organ D 1996 Comput. Meth. Appl. Mech. Engng. 139 3
5. Cheng Y M and Peng M J 2005 Sci. Chin. G: Phys., Mech. Astron. 48 641 (Pubitemid 43322615)
6. Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
7. Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
8. Cheng R J and Cheng Y M 2007 Acta Phys. Sin. 56 5569 (in Chinese)
9. Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
10. Cheng R J and Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese)
11. Cheng R J and Ge H X 2009 Chin. Phys. B 18 4059
12. Wang J F, Sun F X and Cheng R J 2010 Chin. Phys. B 19 060201
13. Cheng R J and Ge H X 2010 Chin. Phys. B 19 090201
14. Cheng Y M and Li J H 2006 Sci. Chin. G: Phys., Mech. Astron. 49 46 (Pubitemid 43322908)
15. Wang J F and Cheng Y M 2011 Chin. Phys. B 20 030206
16. Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
17. Cheng R J and Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese)
18. Cheng R J and Liew K M 2012 Eng. Analysis with Boundary Elements 36 203
19. Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
20. Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
21. Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
22. Cheng Y M, Liew K M and Kitipornchai S 2009 Int. J. Numer. Methods Eng. 78 1258
23. Li S C and Cheng Y M 2004 Chin. J. Theor. Appl. Mech. 36 496
24. Cheng R J and Cheng Y M 2007 Chin. J. Theor. Appl. Mech. 39 843
25. Cheng R J and Ge H X 2012 Chin. Phys. B 21 040203
26. Gao H F and Cheng Y M 2010 Int. J. Comput. Methods 7 55
27. Gao H F and Cheng Y M 2009 Chin. J. Theor. Appl. Mech. 41 480
28. Monaghan J J 1988 Comput. Phys. Commun. 48 89
29. Chen W 2000 Eng. Analysis with Boundary Elements 26 577
30. Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Method Eng. 37 229
31. Liu W K, Jun S and Zhang Y F 1995 Int. J. Numer. Method Fluids 20 1081
32. Cheng R J and Liew K M 2009 Comput. Mech. 45 1
33. Atluri S N and Zhu T 1998 Comput. Mech. 22 117
34. Cheng R J and Cheng Y M 2008 Appl. Numer. Math. 58 884 (Pubitemid 351620963)
35. Morrison P J and Meiss J D 1984 Physica 11D (30) 324
36. George A 1994 Solving Frontier Problems of Physics: Adomain Decomposition Method (Boston: Kluwer Academic Publishers)
37. Parkes E J and Duffy B R 1998 Comput. Phys. Commun. 98 288
38. Khater A H and Malfiet W 2002 Chaos, Solitons Fractals 14 513 (Pubitemid 34182473)
39. Fan E 2000 Phys. Lett. A 277 212 (Pubitemid 32001663)
40. Abdou M A 2006 Physica A 36 394
41. Gao Y T and Tian B 2001 Comput. Phys. Commun. 133 158 (Pubitemid 32072297)
42. Tang X Y and Lou S Y 2002 Chaos, Solitons Fractals 14 1451
43. Wazwaz A M 2005 Appl. Math. Comput. 16 561
44. Ritz W 1909 J. fur Reine Angewandte Mathematik 135 1
45. Rayleigh J W 1877 Theory of Sound vol 1 (New York: Macmillan) (reprinted by Dover Publications in 1945)
46. Kitipornchai S, Xiang Y, Wang C M and Liew K M 1993 Int. J. Numer. Method Eng. 36 299
47. Liew K M, Xiang Y, Wang C M and Kitipornchai S 1993 Comput. Methods Appl. Mech. Eng. 110 301
48. Liew K M, Xiang Y, Kitipornchai S and Meek J L 1995 Comput. Methods Appl. Mech. Eng. 120 339
49. Cheung Y K and Zhou D 2001 Comput.s Structures 79 1923 (Pubitemid 32922961)
50. Cheung Y K and Zhou D 2002 Int. J. Solids Struct. 39 673 (Pubitemid 34254085)
51. Zeng H and Bert C W 2001 Int. J. Stab. Dyn. 1 125
52. Su G H and Xiang Y 2002 Eng. Struc. 24 563 (Pubitemid 34444024)
53. Lim C W and Liew K M 1994 J. Sound Vib. 173 343
54. Liew K M and Feng Z C 2001 Int. J. Mech. Sci. 43 2613 (Pubitemid 32866902)
55. Rubin S G and Graves R A 1975 Comput.s Fluids 3 1
56. Saka B 2006 Appl. Math. Comput. 175 730
57. Esen A 2005 Appl. Math. Comput. 168 65 (Pubitemid 41383643)