WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS' EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (10): 1140-1152.

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS' EQUATION

田立新¹, 许伯强¹, 刘曾荣²

1. Faculty of Science, Jiangsu University of Science and Technology, Zhenjiang 212013, P. R. China;
2. Department of Mathematics, Shanghai University, Shanghai 200018, P. R. China

收稿日期:2001-10-09 修回日期:2002-03-19 出版日期:2002-10-18 发布日期:2002-10-18
基金资助:
the National Natural Science Foundation of China(10071033);the Education Ministry Foundation for Backbone Teachers

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS’ EQUATION

TIAN Li-xin¹, XU Bo-qiang¹, LIU Zeng-rong²

1. Faculty of Science, Jiangsu University of Science and Technology, Zhenjiang 212013, P. R. China;
2. Department of Mathematics, Shanghai University, Shanghai 200018, P. R. China

Received:2001-10-09 Revised:2002-03-19 Online:2002-10-18 Published:2002-10-18
Supported by:
the National Natural Science Foundation of China(10071033);the Education Ministry Foundation for Backbone Teachers

摘要/Abstract

摘要： The existence of approximate inertial manifold using wavelet to Burgers’ equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers’ equation has a good localization property of the numerical solution distinguishably.

关键词: wavelet, wavelet approximate inertial manifold (WAIM), wavelet Galerkin solution, infinite dimensional dynamic system

Abstract: The existence of approximate inertial manifold using wavelet to Burgers’ equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers’ equation has a good localization property of the numerical solution distinguishably.

Key words: wavelet, wavelet approximate inertial manifold (WAIM), wavelet Galerkin solution, infinite dimensional dynamic system

中图分类号:

O175.29

田立新;许伯强;刘曾荣. WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS' EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1140-1152.

TIAN Li-xin;XU Bo-qiang;LIU Zeng-rong. WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS’ EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1140-1152.

[1]	Jizeng WANG, Yonggu FENG, Cong XU, Xiaojing LIU, Youhe ZHOU. Multiresolution method for bending of plates with complex shapes[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 561-582.
[2]	Xiaojing LIU, Youhe ZHOU, Jizeng WANG. Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 863-882.
[3]	N. M. BUJURKE, M. H. KANTLI. Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 881-898.
[4]	Anyang WANG, Hang XU, Qiang YU. Homotopy Coiflets wavelet solution of electrohydrodynamic flows in a circular cylindrical conduit[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 681-698.
[5]	M. HAMID, M. USMAN, R. U. HAQ, Z. H. KHAN, Wei WANG. Wavelet analysis of stagnation point flow of non-Newtonian nanofluid[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(8): 1211-1226.
[6]	Jiaqun WANG, Xiaojing LIU, Youhe ZHOU. A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 275-290.
[7]	Qiang YU, Hang XU. Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1691-1718.
[8]	Cong XU, Jizeng WANG, Xiaojing LIU, Lei ZHANG, Youhe ZHOU. Coiflet solution of strongly nonlinear p-Laplacian equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 1031-1042.
[9]	吴彦华;任慧颖. Analysis of realistic rough surface for its globally dominant parameters using continuous wavelets[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 741-748.
[10]	刘小靖王记增王晓敏周又和. Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(1): 49-62.
[11]	Y. S. KIM;陈立群. Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(7): 801-810.
[12]	赵勇宗智邹文楠. Numerical simulation of vortex evolution based on adaptive wavelet method[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(1): 33-44.
[13]	丁亮韩波刘家琦. A wavelet multiscale method for inversion of Maxwell equations[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(8): 1035-1044.
[14]	夏振炎田砚姜楠. Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 435-443.
[15]	向家伟陈雪峰李锡夔. Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(10): 1325-1334.

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS' EQUATION

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS’ EQUATION

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