| 一类抛物方程正交小波基的构造 |
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| 引用本文： | 赵建斌,罗迪凡,喻海元,尹伊.一类抛物方程正交小波基的构造[J].衡阳工学院学报,2010(2):68-73. |
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| 作者姓名： | 赵建斌 罗迪凡 喻海元 尹伊 |
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| 作者单位： | [1]滨州学院计算机科学技术系,山东滨州256603 [2]南华大学数理学院,湖南衡阳421001 [3]湘潭大学数学与计算科学学院,湖南湘潭411105 [4]广州市第113中学,广东广州510630 |
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| 摘 要： | 对抛物方程右端项关于时间变量先作小波展开，化为多个可以并行的椭圆方程求解，是国际上近些年来发展起来的一种新的数值求解方法．本文利用勒让德多项式构造出了一类适合的正交小波基，并给出了一般情况下的小波系数递推公式．数值例子验证了递推公式的有效性．
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| 关 键 词： | 抛物方程 正交小波基 小波系数 递推公式 |
Construction of a Class of Orthogonal Wavelet Bases about Parabolic Equations |
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| Authors: | ZHAO Jian-bin LUO Di-fan YU Hai-yuan YIN Yi |
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| Affiliation: | 1. Department of Computer Science and Technology, Binzhou University, Binzhou, Shandong 256603, China; 2. School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China; 3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China; 4.113 Middle School, Guangzhou 510630, China) |
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| Abstract: | In recent years, some foreign scholars have develop a new method for the numerical solution of PPDEs. As the first step the method uses wavelet bases to decompose the forcing term, so the problem is transformed into some elliptic PDEs which can be solved by parallel algorithm. In this paper, we will construct a class of Orthogonal Wavelet Bases, and present the general recurrence formula of wavelet coefficients. The numerical test convinces our analysis. |
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| Keywords: | parabolic differential equations orthogonal wavelet bases wavelet coefficients recurrence formula |
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