基于同伦技术的Burgers方程的小波精细积分算法

计算物理 ›› 2007, Vol. 24 ›› Issue (1): 54-58.

基于同伦技术的Burgers方程的小波精细积分算法

梅树立¹, 张森文², 陆启韶³

1. 中国农业大学信息与电气工程学院, 北京 100083;
2. 暨南大学应用力学研究所, 广州石牌 510632;
3. 北京航空航天大学理学院, 北京 100083

收稿日期:2005-08-01 修回日期:2005-12-13 出版日期:2007-01-25 发布日期:2007-01-25
作者简介:梅树立(1968-),男,河北元氏,博士,副教授,从事计算力学方面的研究,北京市海淀区清华东路17号,中国农业大学东区53信箱100083.
基金资助:
国家自然科学基金(10372036);中国农业大学科研启动基金(2005037)资助项目

A Wavelet Precise Integration Method for Burgers Equations Based on Homotopy Technique

MEI Shuli¹, ZHANG Senwen², LU Qishao³

1. College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China;
2. The Institute of Applied Mechanics, Jinan University, Guangzhou 510632, China;
3. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Received:2005-08-01 Revised:2005-12-13 Online:2007-01-25 Published:2007-01-25

摘要/Abstract

摘要： 以Burgers方程为例,结合区间小波精细积分方法,将同伦摄动方法的应用范围推广到多维非线性问题,给出一种求解非线性偏微分方程的新的小波精细积分方法,得到一种近似解析解的数值结果,对时间步长不敏感,更适合于求解非线性问题.

关键词: 同伦摄动法, 精细积分法, 非线性偏微分方程, 插值小波

Abstract: Taking the Burgers equation as an example,an interval wavelet precise integration method (PIM) for nonlinear PDEs is proposed.The homotopy perturbation method (HPM) for nonlinear problems is adopted.It extends the application of HPM from one dimension to multi-dimensions.As an asymptotic analytical method,it is not sensitive to the time step and is suitable for nonlinear equations.

Key words: homotopy perturbation method, precise integration method, nonlinear partial differential equation, interpolating wavelet

中图分类号:

O351.2

梅树立, 张森文, 陆启韶. 基于同伦技术的Burgers方程的小波精细积分算法[J]. 计算物理, 2007, 24(1): 54-58.

MEI Shuli, ZHANG Senwen, LU Qishao. A Wavelet Precise Integration Method for Burgers Equations Based on Homotopy Technique[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 24(1): 54-58.