ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (10): 1168-1183.

ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

尚亚东¹, 郭柏灵²

1. Department of Mathematics, Guangzhou University, Guangzhou 510405, P. R. China;
2. Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, P. R. China

收稿日期:2001-11-27 修回日期:2003-05-16 出版日期:2003-10-18 发布日期:2003-10-18
基金资助:
the National Natural Science Foundation of China(10271034)

ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

SHANG Ya-dong¹, GUO Bo-ling²

1. Department of Mathematics, Guangzhou University, Guangzhou 510405, P. R. China;
2. Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, P. R. China

Received:2001-11-27 Revised:2003-05-16 Online:2003-10-18 Published:2003-10-18
Supported by:
the National Natural Science Foundation of China(10271034)

摘要/Abstract

摘要： The Chebyshev pseudospectral approximation of the homogeneous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained.

中图分类号:

O241

尚亚东;郭柏灵. ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1168-1183.

SHANG Ya-dong;GUO Bo-ling. ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1168-1183.

参考文献

[1] Seyler C E, Fanstermacler D C. A symmetric regularized long wave equation[J]. Phys Fluids,1984,27(1) :4-7.
[2] Iskandar L, Jain P C. Numerical solutions of the improved Boussinesq equation[J]. Proc Indian Acad Sci Math Sci, 1980,89(1): 171-181.
[3] Soerensen M P, Christainsen P L, Lomdahl P S. Solitary waves on nonlinear elastic rods[J]. J Acoust Soc Amer , 1984,76(5): 871-879.
[4] Bogolubsky J L. Some examples of inelastic soliton interaction[J]. Comput Phys Comm, 1977,13(1): 149-155.
[5] CHEN Lin. Stability and instability of solitary waves tor generalized symmetric regularized long wave equations[J]. Physica D, 1998,118(1/2): 53-68.
[6] GUO Bo-ling. The spectral method for symmetric regularized wave equations[J]. J Comput Math,1987,5(4) :297-306.
[7] ZHENG Jia-dong,ZHANG Ru-fen,GUO Ben-yu. The Fourier pseudo-spectral method for SRLW equation[J]. Applied Mathematics and Mechanics (English Edition), 1989,10 (9): 843-852.
[8] ZHENG Jia-dong. The pseudospectral collocation method for the generalized SRLW equations[J].Numer Math Sinica, 1989,11(1): 64-72. (in Chinese)
[9] GUO Bo-ling. The existence of global solutions and" blow up" phenomena for a system of multidimensional symmetric regularized wave equations[J]. Acta Math Appl Sinica, 1992,8(1):59-72.
[10] SHANG Ya-dong, LIZhi-shen. The Fourier spectral methods for solving the multidimensional generalized symmetric regularized long wave equations[J]. Mumer Math-A Journal of Chinese University, 1999,21(1) :48-60. (in Chinese)
[11] MA He-ping, GUO Ben-yu. The Chebyshev spectral methods for Burgers-like equations[J]. J Comput Math, 1988,6(1): 51-56.
[12] Bressan N, Quarteroni A. Analysis of Chebyshev collocation methods for parabolic equations[J].SIAM J Numer Anal, 1986,23(6): 1138-1154.
[13] Canuto C, Hussaini M Y, Quarteroni A, et al. Spectral Methods in Fluid Dynamics[M]. New York: Springer-Verlag, 1988.
[14] XIANG Xin-ming, ZHANG Fa-yong. Chebyshev pseudospectral method for the generalized BBM equations in higher dimension[J]. Numer Math Sinica, 1991,13(4) :403-411. (in Chinese)
[15] GUO Ben-yu. Spectral Methods and Their Applications[M]. Singapore: World Scientific, 1998.

ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Wei SU, Zhenyu TANG, Bijiao HE, Guobiao CAI. Stable Runge-Kutta discontinuous Galerkin solver for hypersonic rarefied gaseous flow based on 2D Boltzmann kinetic model equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 343-362.
[2]	Zhendong LUO, Fei TENG. Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 289-310.
[3]	Jing ZHU, Shengnan WANG, Liancun ZHENG, Xinxin ZHANG. Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(1): 125-136.
[4]	Jing ZHU, Liu ZHENG, Liancun ZHENG, Xinxin ZHANG. Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1131-1146.
[5]	Benwen LI, Shangshang CHEN. Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 1073-1090.
[6]	Guodong ZHANG, Xiaojing DONG, Yongzheng AN, Hong LIU. New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 863-872.
[7]	M. NAZARI;H. SHOKRI;A. A. MOHAMAD. Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(4): 523-540.
[8]	Yirang YUAN;Aijie CHENG;Danping YANG;Changfeng LI;Yunxin LIU. Theory and application of numerical simulation method of capillary force enhanced oil production[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 379-400.
[9]	N. ZHAO;K. IRAMINA. Numerical simulation of effect of convection-diffusion on oxygen transport in microcirculation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(2): 179-200.
[10]	S. MANSUR;A. ISHAK;I.POP. Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1401-1410.
[11]	A. ABEDIAN;J. PARVIZIAN;A. D�STER;E. RANK. Finite cell method compared to h-version finite element method for elasto-plastic problems[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1239-1248.
[12]	袁益让;李长峰;孙同军;刘允欣. Characteristic fractional step finite difference method for nonlinear section coupled system[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1311-1330.
[13]	朱玮;舒适;成礼智. First-order optimality condition of basis pursuit denoise problem[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1345-1352.
[14]	刘建康;郑洲顺. Efficient high-order immersed interface methods for heat equations with interfaces[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1189-1202.
[15]	葛全文. High-order Lagrangian cell-centered conservative scheme on unstructured meshes[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1203-1222.