| 偏微分方程的样条小波及替代算法 |
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| 引用本文： | 郑宏兴.偏微分方程的样条小波及替代算法[J].宁夏大学学报(自然科学版),2001,22(1):1-4,10. |
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| 作者姓名： | 郑宏兴 |
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| 作者单位： | 宁夏大学,数学与电算工程系, |
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| 基金项目： | 国防科技预研基金资助项目!(J 3.2 .5 .4) |
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| 摘 要： | 研究了三次样条插值的小波插值函数，证明了在给定的插值节点上的小波插值函数是三次样条函数空间中的最佳逼近函数，给出插值函数的误差估计式，提出了用两个一阶导算子矩阵替代二阶导算子矩阵的替代算法，并对Burgers方程进行了验算。
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| 关 键 词： | 样条小波 插值算法 导算子逼近 偏微分方程 替代算法 导算子矩阵 小波配点法 插值函数 |
| 文章编号： | 0253-2328(2001)01-0001-04 |
Solution of partial differential equation with cubic spline interval wavelet and differential approximation |
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| ZHENG Hong-xing.Solution of partial differential equation with cubic spline interval wavelet and differential approximation[J].Journal of Ningxia University(Natural Science Edition),2001,22(1):1-4,10. |
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| Authors: | ZHENG Hong-xing |
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| Abstract: | The optimal approximation property is shown when the cubic spline interval wavelet is used in the interpolation with some special points. This property ensures the identical of the interpolation by use of scale basis and of wavelet basis. The interpolation error is also discussed. A new algorithm is presented in which two one-order differential matrixes are used to substitute for the two-order one. This way produces less vibration for the numerical solution of Burgers equation when the coefficient is somewhat larger. |
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| Keywords: | spline wavelet interpolation algorithm differential approximation |
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