| 用径向基函数解偏微分方程 |
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| 引用本文： | 张颖超. 用径向基函数解偏微分方程[J]. 湖南师范大学自然科学学报, 2011, 34(5): 1-6 |
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| 作者姓名： | 张颖超 |
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| 作者单位： | 广西师范大学数学科学学院,中国桂林,541004 |
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| 基金项目： | 国家自然科学基金资助项目(11171102) |
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| 摘 要： | 讨论了用正定径向基函数解偏微分方程,通过一个数值算例,说明这个方法是可行的.针对数值算例,比较了在相同步长时,不同的正定径向基函数对微分方程数值解的精确程度,并比较不同的正定径向基函数在相同的形状参数时绝对误差的差异,说明微分方程数值解的精确程度与径向基函数形状参数的取值密切相关.同时也论证了在插值过程中所得到的矩阵方...
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| 关 键 词： | 径向基函数 数值解 偏微分方程 线性无关 |
Application of Radial Basis Functions for Partial Differential Equations |
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| ZHANG Ying-chao. Application of Radial Basis Functions for Partial Differential Equations[J]. Journal of Natural Science of Hunan Normal University, 2011, 34(5): 1-6 |
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| Authors: | ZHANG Ying-chao |
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| Affiliation: | ZHANG Ying-chao*(School of Mathematics,Guangxi Normal University,Guilin 541004,China) |
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| Abstract: | An algorithm for partial differential equations based on the positive definite radial basis funtions(RBF) approximation scheme is presented.One model problem of the algorithm is given.The comparison is made with the exact solutions of the problem by different shape parameter when different radial basis functions are chosen.Numerical results show that method offers a very high accuracy in computation of the partial differential equation.It shows that choice of shape parameter is important.The obtained coeffi... |
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| Keywords: | RBF numerical solutions partial differential equation linear independent |
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