| 二维偏微分方程的小波配点法 |
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| 引用本文： | 张培茹,赵凤群,周千,何静.二维偏微分方程的小波配点法[J].西安理工大学学报,2010,26(1):121-125. |
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| 作者姓名： | 张培茹 赵凤群 周千 何静 |
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| 作者单位： | 西安理工大学理学院,陕西,西安,710054 |
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| 摘 要： | 根据多分辨分析,使用任意连续的尺度函数,在边界处结合外尺度函数,构造了区间上的插值基函数,并结合二元张量积小波分析将此方法推广到了二维.同时,给出了边值条件的积分处理方法,形成了求解二维偏微分方程的小波配点法.以二维热传导方程定解问题为例,选择Shannon函数进行了数值计算.结果表明,数值解达到了较高的精度,表明该方法适用于高维情形.
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| 关 键 词： | 多分辨分析 插值基函数 二元张量积 二维热传导方程 |
A Wavelet Collocation Method for Solving the Two-Dimensional Heat Equation |
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| ZHANG Pei-ru,ZHAO Feng-qun,ZHOU Qian,HE Jing.A Wavelet Collocation Method for Solving the Two-Dimensional Heat Equation[J].Journal of Xi'an University of Technology,2010,26(1):121-125. |
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| Authors: | ZHANG Pei-ru ZHAO Feng-qun ZHOU Qian HE Jing |
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| Institution: | ZHANG Pei-ru,ZHAO Feng-qun,ZHOU Qian,HE Jing (Faculty of Sciences,Xi\'an University of Technology,Xi\'an 710054,China) |
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| Abstract: | Based on multi-resolution analysis,the interpolation base functions in interval is proposed,by using arbitrary continuous scaling function and external scaling function in the boundry.And then this method is extended to two-dimensional function in combination with two-tensor product wavelet analysis.At the same time,an integral approach of dealing with boundary condition is suggested,whereby forming a wavelet collocation method for solving the two-dimensional differential equation.At last,taking the two-dim... |
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| Keywords: | multi-resolution analysis interpolation base function two-tensor product two-dimensional heat equation |
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