[1]李敏,庄清渠.半无界条状区域四阶方程的Laguerre-Legendre混合谱逼近[J].华侨大学学报(自然科学版),2013,34(4):471-476.[doi:10.11830/ISSN.1000-5013.2013.04.0471]
　LI Min,ZHUANG Qing-qu.Mixed Laguerre-Legendre Spectral Approximation of the Fourth-Order Equations in a Semi-Infinite Channel[J].Journal of Huaqiao University(Natural Science),2013,34(4):471-476.[doi:10.11830/ISSN.1000-5013.2013.04.0471]
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半无界条状区域四阶方程的Laguerre-Legendre混合谱逼近()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第4期
页码:
471-476
栏目:
出版日期:
2013-07-20

文章信息/Info

Title:
Mixed Laguerre-Legendre Spectral Approximation of the Fourth-Order Equations in a Semi-Infinite Channel
文章编号:
1000-5013(2013)04-0471-06
作者:
李敏;  庄清渠
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LI Min;  ZHUANG Qing-qu
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
四阶方程;  半无界条状区域;  Laguerre-Legendre混合谱;  基函数;  收敛性
Keywords:
fourth-order equations;  semi-infinite channel;  mixed Laguerre-Legendre spectral method;  basis function;  convergence
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.2013.04.0471
文献标志码:
A
摘要:
对二维半无界条状区域上的四阶偏微分方程,用不带权函数的Laguerre-Legendre混合谱方法进行逼近.通过构造满足微分方程边界条件的基函数,由离散变分公式可以得到具有稀疏系数矩阵的代数系统,从而有效地进行求解.对该方法进行严格的收敛性分析,数值结果验证了方法的收敛性和有效性.
Abstract:
Mixed Laguerre-Legendre spectral method without weight function is presented to solve the fourth-order equations in a semi-infinite channel. By constructing appropriate basis functions satisfying the boundary conditions, the coefficient matrix of the corresponding linear system is sparse, and the solution can be solved efficiently. Rigorous analysis of the convergence of this method is carried out. Numerical experiments are given to confirm the convergence and efficiency of the method.

参考文献/References:

[1] GUO Ben-yu,SHEN Jie.Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval[J].Numerische Mathematik,2000,86(4):635-654.
[2] SHEN Jie.Stable and efficient spectral methods in unbounded domains using laguerre functions[J].SIAM Journal on Numerical Analysis,2001,38(4):1113-1133.
[3] 王志焕.一类自由边界问题解的渐近性[J].华侨大学学报:自然科学版,2006,27(2):133-136.
[4] WANG Li-lian,GUO Ben-yu.Stair Laguerre pseudospectral method for differential equations on the half line[J].Advances in Computational Mathematics,2006,25(1):305-322.
[5] 叶小华.四阶方程的Legendre-Laguerre复合谱方法[J].吉林师范大学学报:自然科学版,2009,30(2):122-128.
[6] GUO Ben-yu,MA He-ping.Composite Legendre-Laguerre approximation in unbounded domains[J].Journal of Computational Mathematics,2001,19(1):101-112.
[7] GUO Ben-yu,WANG Li-lian.Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation[J].Journal of Computational and Applied Mathematics,2006,190(1):304-324.
[8] SHEN Jie,WANG Li-lian.Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations[J].Discrete and Continuous Dynamical Systems Series B,2006,6(6):1381-1402.
[9] ZHUANG Qing-qu,XU Chuan-ju.Legendre-Laguerre coupled spectral element methods for second- and fourth-order equations on the half line[J].Journal of Computational and Applied Mathematics,2010,235(3):615-630.
[10] GUO Ben-yu,XU Cheng-long.Mixed Laguerre-Legendre pseudospectral method for incompressible fiow in an infinite strip[J].Mathematics of computation,2004,73(245):95-126.
[11] GUO Ben-yu,WANG Tian-jun.Composite Laguerre-Legendre spectral method for fourth-order exterior problems[J].Journal of Scientific Computing,2010,44(3):255-285.
[12] WANG Zhong-qin,GUO Ben-yu.A mixed spectral method for incompressible vis cous fiuid fiow in an infinite strip[J].Journal of Computational and Applied Mathematics,2005,24(3):343-346.
[13] XU Cheng-long,GUO Ben-yu.Mixed Laguerre-Legendre spectral method for incompressible flow in an infinite strip[J].Advances in Computational Mathematics,2002,16(1):77-96.
[14] BERNARDI C,MADAY Y.Approximations spectrales de problemes aux limites elliptiques[M].Paris:Springer-Verlag,1992:21-27.
[15] SHEN Jie,WANG Li-lian.Some recent advances on spectral methods for unbounded domains[J].Communications in Computational Physics,2009,5(2/3/4):195-241.

相似文献/References:

[1]蔡耀雄,庄清渠.全直线上四阶方程的Laguerre-Laguerre复合谱逼近[J].华侨大学学报(自然科学版),2021,42(2):275.[doi:10.11830/ISSN.1000-5013.202009051]
　CAI Yaoxiong,ZHUANG Qingqu.Composite Laguerre-Laguerre Spectral Method for Fourth-Order Equation on Whole Line[J].Journal of Huaqiao University(Natural Science),2021,42(4):275.[doi:10.11830/ISSN.1000-5013.202009051]

备注/Memo

备注/Memo:
收稿日期: 2012-06-29
通信作者: 庄清渠(1980-),男,讲师,主要从事微分方程数值解法的研究.E-mail:qqzhuang@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11126330); 福建省自然科学基金资助项目(2011J05005)
更新日期/Last Update: 2013-07-20