| 解一维及多维非线性发展方程的小波方法 |
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| 引用本文： | 郭琦,吴勃英,杨永田.解一维及多维非线性发展方程的小波方法[J].哈尔滨工业大学学报,2009(11):99-102. |
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| 作者姓名： | 郭琦 吴勃英 杨永田 |
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| 作者单位： | 哈尔滨工业大学数学系;哈尔滨工程大学计算机系 |
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| 基金项目： | 黑龙江省博士后基金资助项目 |
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| 摘 要： | 给出了求解一维及多维的非线性发展方程的小波方法,解决了多维非线性发展方程具有周期性边界条件的小波求解问题.由于小波函数的局部性,在处理奇异性问题比古典方法要好得多,该方法比差分法、有限元、谱方法等具有更高的求解精度.数值结果表明该方法是非常准确和有效的.
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| 关 键 词： | 小波 一维 多维 非线性发展方程 |
Wavelet method for solving one-dimensional and multi-dimensional nonlinear evolution equations |
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| GUO Qi,WU Bo-ying,YANG Yong-tian.Wavelet method for solving one-dimensional and multi-dimensional nonlinear evolution equations[J].Journal of Harbin Institute of Technology,2009(11):99-102. |
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| Authors: | GUO Qi WU Bo-ying YANG Yong-tian |
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| Affiliation: | 1. Dept. of Mathematics,Harbin Institute of Technology,Harbin 150001,China; 2. School of Computer Science and Engineering,Harbin University of Engineering,Harbin 150001,China) |
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| Abstract: | A wavelet method for solving one-dimensional and multi-dimensional nonlinear evolution equations is presented. It offers a way to solve the multi-dimensional nonlinear evolution equations with periodic boundary conditions using wavelet. Due to the local property of wavelet function,this method can deal with the singularity better than classical methods. And it has higher accuracy than classical methods used commonly,such as the difference method,the finite element,the spectral method,etc. The numerical results show that the presented method is accurate and efficient. |
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| Keywords: | wavelet one dimension multi-dimension nonlinear evolution equation |
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