求解非线性偏微分方程的自适应小波精细积分法

计算物理 ›› 2004, Vol. 21 ›› Issue (6): 523-530.

求解非线性偏微分方程的自适应小波精细积分法

梅树立¹, 陆启韶¹, 张森文²

1. 北京航空航天大学理学院, 北京 100083;
2. 暨南大学应用力学研究所, 广东广州 510632

收稿日期:2003-09-08 修回日期:2004-01-08 出版日期:2004-11-25 发布日期:2004-11-25
作者简介:梅树立(1968-),男,河北元氏,博士后,从事计算力学方面的研究.
基金资助:
国家自然科学基金(10372036);广东省自然科学基金(021197)资助项目

An Adaptive Wavelet Precise Integration Method for Partial Differential Equations

MEI Shu-li¹, LU Qi-shao¹, ZHANG Sen-wen²

1. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. The Institute of Applied Mechanics, Jinan University, Guangzhou 510632, China

Received:2003-09-08 Revised:2004-01-08 Online:2004-11-25 Published:2004-11-25

摘要/Abstract

摘要： 以Burgers方程为例,提出了一种求解偏微分方程的自适应多层插值小波配置法,通过引入一种具有插值特性的拟Shannon小波并利用插值小波理论构造了多层自适应插值小波算子,从而在空间实现了偏微分方程的自适应离散.另外,精细时程积分方法和外推法的引入不但有助于提高求解速度和数值结果的精度,而且使时间积分步长的选取具有了自适应性.

关键词: 非线性偏微分方程, 拟Shannon小波, 自适应多层插值, 精细时程积分

Abstract: Taking the Burgers equation as example, an adaptive multilevel interpolation quasi-wavelet collocation method for the solution of partial differential equations is developed. In this method, an adaptive multilevel quasi-wavelet collocation interpolation operator is constructed according to the interpolation wavelet theory, and then the equations can be discreted adaptively in physical space. On the other hand, the extrapolation and precise integration method is helpful for decreasing computation time and improving calculating precision, and it make the selection of time step for integration self-adaptive.

Key words: nonlinear partial differential equations, quasi Shannon wavelets, adaptive multilevel interpolation, precise time-integration

中图分类号:

O351.2

梅树立, 陆启韶, 张森文. 求解非线性偏微分方程的自适应小波精细积分法[J]. 计算物理, 2004, 21(6): 523-530.

MEI Shu-li, LU Qi-shao, ZHANG Sen-wen. An Adaptive Wavelet Precise Integration Method for Partial Differential Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 21(6): 523-530.