| 抛物型方程的Shannon小波配点法 |
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| 引用本文： | 史策.抛物型方程的Shannon小波配点法[J].咸阳师范学院学报,2012,27(2):11-13. |
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| 作者姓名： | 史策 |
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| 作者单位： | 陕西教育学院,陕西西安,710100 |
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| 摘 要： | 利用Shannon小波配点法对一维抛物型方程进行求解,将一维Shannon尺度函数引入到抛物型方程求解中,选取一个适当的加窗基函数,给出了一维抛物型方程解的近似表达式,运用小波配点法对一维抛物型方程进行空间离散,将该问题转化为常微分方程组,利用龙格-库塔法对方程组进行数值求解。数值解结果显示,所采用的方法其数值解具有比较高的精度。
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| 关 键 词： | 抛物型偏微分方程 数值解 Shannon小波 配点法 小波基 |
Shannon Wavelet Collocation Method for Solving PDEs of Parabolic Type |
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| SHI Ce.Shannon Wavelet Collocation Method for Solving PDEs of Parabolic Type[J].Journal of Xianyang Normal University,2012,27(2):11-13. |
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| Authors: | SHI Ce |
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| Institution: | SHI Ce(Shaanxi Institute of Education,Xi’an 710100,Shaanxi,China) |
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| Abstract: | This paper is the use of Shannon wavelet collocation method for one-dimensional parabolic equation solving.The Shannon scaling function of one-dimensional was introduced to solve the parabolic equation.The appropriate windowed basis function was selected,and the approximation expression of one-dimensional parabolic equation was given.Furthermore,one-dimensional parabolic equation was spatially discretized by wavelet collocation method and transformed to differential equations,which could be solved by Rungc-Kutta method.The results show that the method used in this paper has a good accuracy. |
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| Keywords: | partial differential equations of parabolic type numerical solution Shannon wavelet collocationmethod wavelet base |
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