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

doi:10.1088/1674-1056/21/10/100209

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100209-100209.doi: 10.1088/1674-1056/21/10/100209

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

程荣军^a, 葛红霞^b

a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
b Faculty of Science, Ningbo University, Ningbo 315211, China

收稿日期:2012-03-04 修回日期:2012-04-09 出版日期:2012-09-01 发布日期:2012-09-01
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007).

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

Cheng Rong-Jun (程荣军)^a, Ge Hong-Xia (葛红霞)^b

a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
b Faculty of Science, Ningbo University, Ningbo 315211, China

Received:2012-03-04 Revised:2012-04-09 Online:2012-09-01 Published:2012-09-01
Contact: Cheng Rong-Jun E-mail:chengrongjun76@126.com
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007).

摘要/Abstract

摘要： In this paper, we analyse the equal width (EW) wave equation by using the mesh-free reproducing kernel particle Ritz (kp-Ritz) method. The mesh-free kernel particle estimate is employed to approximate the displacement field. A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions. The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.

关键词: meshless method, mesh-free kp-Ritz method, equal width (EW) wave equation, solitary wave

Abstract: In this paper, we analyse the equal width (EW) wave equation by using the mesh-free reproducing kernel particle Ritz (kp-Ritz) method. The mesh-free kernel particle estimate is employed to approximate the displacement field. A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions. The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.

Key words: meshless method, mesh-free kp-Ritz method, equal width (EW) wave equation, solitary wave

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

03.65.Ge (Solutions of wave equations: bound states)

程荣军, 葛红霞. Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method[J]. 中国物理B, 2012, 21(10): 100209-100209.

Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞). Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method[J]. Chin. Phys. B, 2012, 21(10): 100209-100209.

参考文献 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 A1983 Nucl. Eng. Des. 76 47
[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. m & Astron. 48 641
[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. m & Astron. 49 46
[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 Engineering 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 Engineering Analysis with Boundary Elements 26 577
[30]	Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[31]	Liu W K, Jun S and Zhang Y F 1995 Int. J. Numer. Meth. Eng. 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
[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 and Fractals 14 513
[39]	Fan E 2000 Phys. Lett. A 277 212
[40]	Abdou M A 2006 Physica A 36 394
[41]	Gao Y T and Tian B 2001 Comput. Phys. Commun. 133 158
[42]	Tang X Y and Lou S Y 2002 Chaos, Solitons and Fractals 14 1451
[43]	Wazwaz A M 2005 Appl. Math. Comput. 16 561
[44]	Ritz W 1909 Journal fur Reine and 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 Computers and Structures 79 1923
[50]	Cheung Y K and Zhou D 2002 Int. J. Solids Struct. 39 673
[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
[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
[55]	Rubin S G and Graves R A1975 Computers and Fluids 3 1
[56]	Saka B 2006 Appl. Math. Comput. 175 730
[57]	Esen A 2005 Appl. Math. Comput. 168 65

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

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 57

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Bin He(何斌) and Qing Meng(蒙清). Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation[J]. 中国物理B, 2021, 30(6): 60201-060201.
[2]	Serge Bruno Yamgoué, Guy Roger Deffo, Eric Tala-Tebue, François Beceau Pelap. Exact transverse solitary and periodic wave solutions in a coupled nonlinear inductor-capacitor network[J]. 中国物理B, 2018, 27(9): 96301-096301.
[3]	宋宗斌, 杨雪滢, 封文星, 席忠红, 李烈娟, 石玉仁. Decaying solitary waves propagating in one-dimensional damped granular chain[J]. 中国物理B, 2018, 27(7): 74501-074501.
[4]	D M S Zaman,M Amina,P R Dip,A A Mamun. Nucleus-acoustic solitary waves in self-gravitating degenerate quantum plasmas[J]. 中国物理B, 2018, 27(4): 40402-040402.
[5]	王扶刚, 杨阳阳, 韩娟芳, 段文山. Head-on collision between two solitary waves in a one-dimensional bead chain[J]. 中国物理B, 2018, 27(4): 44501-044501.
[6]	马立媛, 季佳梁, 徐宗玮, 朱佐农. Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays[J]. 中国物理B, 2018, 27(3): 30201-030201.
[7]	马吉超, 魏高峰, 刘丹丹. Improved reproducing kernel particle method for piezoelectric materials[J]. 中国物理B, 2018, 27(1): 10201-010201.
[8]	杜文青, 孙建安, 杨阳阳, 段文山. Envelope solitary waves and their reflection and transmission due to impurities in a granular material[J]. 中国物理B, 2018, 27(1): 14501-014501.
[9]	吴意, 马永其, 冯伟, 程玉民. Topology optimization using the improved element-free Galerkin method for elasticity[J]. 中国物理B, 2017, 26(8): 80203-080203.
[10]	Melis Zorsahin Gorgulu,Idris Dag,Dursun Irk. Simulations of solitary waves of RLW equation by exponential B-spline Galerkin method[J]. 中国物理B, 2017, 26(8): 80202-080202.
[11]	王振, 秦玉鹏, 邹丽. Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation[J]. 中国物理B, 2017, 26(5): 50504-050504.
[12]	吴锋, 姚征, 钟万勰. Fully nonlinear (2+1)-dimensional displacement shallow water wave equation[J]. 中国物理B, 2017, 26(5): 54501-054501.
[13]	唐耀宗, 李小林. Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems[J]. 中国物理B, 2017, 26(3): 30203-030203.
[14]	李近元, 方念乔, 张吉, 薛玉龙, 王雪木, 袁晓博. (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect[J]. 中国物理B, 2016, 25(4): 40202-040202.
[15]	陈莘莘, 王娟, 李庆华. Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method[J]. 中国物理B, 2016, 25(4): 40203-040203.