An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

doi:10.1088/1674-1056/22/7/074704

中国物理B ›› 2013, Vol. 22 ›› Issue (7): 74704-074704.doi: 10.1088/1674-1056/22/7/074704

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

冯昭, 王晓东, 欧阳洁

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

收稿日期:2012-10-11 修回日期:2013-01-08 出版日期:2013-06-01 发布日期:2013-06-01
基金资助:
Project supported by the National Basic Research Program of China (Grant No. 2012CB025903).

An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

Feng Zhao (冯昭), Wang Xiao-Dong (王晓东), Ouyang Jie (欧阳洁)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2012-10-11 Revised:2013-01-08 Online:2013-06-01 Published:2013-06-01
Contact: Ouyang Jie E-mail:jieouyang@nwpu.edu.cn
Supported by:
Project supported by the National Basic Research Program of China (Grant No. 2012CB025903).

摘要/Abstract

摘要： In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method.

关键词: element-free Galerkin method, shifted polynomial basis, generalized fifth-order Korteweg-de Vries equation, solitary wave

Abstract: In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method.

Key words: element-free Galerkin method, shifted polynomial basis, generalized fifth-order Korteweg-de Vries equation, solitary wave

中图分类号: (Solitary waves)

47.35.Fg

04.30.Nk (Wave propagation and interactions) 02.70.Dh (Finite-element and Galerkin methods) 47.10.ab (Conservation laws and constitutive relations)

冯昭, 王晓东, 欧阳洁. An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation[J]. 中国物理B, 2013, 22(7): 74704-074704.

Feng Zhao (冯昭), Wang Xiao-Dong (王晓东), Ouyang Jie (欧阳洁). An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation[J]. Chin. Phys. B, 2013, 22(7): 74704-074704.

参考文献 23

[1]	Kawahara T 1972 J. Phys. Soc. Jpn. 33 260
[2]	Benjamin T B, Bona J L and Mahony J J 1972 Phil. Trans. R. Soc. 272 47
[3]	Hereman W and Nuseir A 1997 Math. Comput. Simul. 43 13
[4]	Tam H W and Hu X B 2000 Phys. Lett. A 272 174
[5]	Lnc M 2006 Appl. Math. Comput. 172 72
[6]	Fan E 2003 Chaos Soliton. Fract. 16 819
[7]	Wazwaz A M 2007 Appl. Math. Comput. 184 1002
[8]	Xin Y, Gao Y T, Sun Z Y and Liu Y 2010 Phys. Scr. 81 045402
[9]	Mohyud-Din S T, Negahdary E and Usman M 2012 Int. J. Numer. Method H 22 641
[10]	Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Methods Eng. 37 229
[11]	Liu G R and Gu Y T 2005 An Introduction to Meshfree Methods and Their Programming (Netherlands: Springer) pp. 102-106
[12]	Zhang L, Ouyang J and Zhang X H 2008 Phys. Lett. A 372 5625
[13]	Zhang X H, Ouyang J and Zhang L 2009 Eng. Anal. Bound. Elem. 33 356
[14]	Wang J F, Sun F X and Cheng R J 2010 Chin. Phys. B 19 060201
[15]	Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[16]	Cheng R J and Ge H X 2012 Chin. Phys. B 21 040203
[17]	Jin X Z, Li G and Aluru N R 2001 Comput. Model. Eng. Sci. 2 447
[18]	Fernánez-Méndez S and Huerta A 2004 Comput. Methods Appl. Mech. Eng. 193 1257
[19]	Belytschko T, Krongauz Y and Organ D 1996 Comput. Methods Appl. Mech. Eng. 139 3
[20]	Yang L, Zhang F J and Wang Y H 2002 Chaos Soliton. Fract. 13 337
[21]	Uddin M, Haq S and Islam S U 2009 Appl. Math. Comput. 212 458
[22]	Parker A 2000 Physica D 137 25
[23]	Goktas U and Hereman W 1997 J. Symb. Comput. 24 591

An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 23

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]	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.
[5]	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.
[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]	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.
[8]	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.
[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]	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.
[11]	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.
[12]	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.
[13]	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.
[14]	陈耀登, 杨红卫, 高玉芳, 尹宝树, 冯兴如. A new model for algebraic Rossby solitary waves in rotation fluid and its solution[J]. 中国物理B, 2015, 24(9): 90205-090205.
[15]	Reza Mohammadi. Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation[J]. 中国物理B, 2015, 24(5): 50206-050206.