| 求解椭圆方程的径向基无网格配置法 |
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| 引用本文： | 向娟,秦新强,徐婷婷,党发宁.求解椭圆方程的径向基无网格配置法[J].世界科技研究与发展,2009,31(4):718-721. |
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| 作者姓名： | 向娟 秦新强 徐婷婷 党发宁 |
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| 作者单位： | 1. 西安理工大学理学院,西安,710048
2. 西安理工大学水利水电学院,西安,710048 |
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| 基金项目： | 国家自然科学基金项目，陕西省教育厅自然科学研究项目 |
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| 摘 要： | 针对一、二维椭圆方程构造了径向基无网格配置法；给出了解的存在唯一性；同时得到了基函数中自由参数c与求解精度的关系，以及节点均布时自由参数最佳取值的计算公式。将节点均布下得到的自由参数取值公式应用于节点任意排列的情况，其求解精度仍能得到保证，表明这种无网格方法对节点的位置不敏感。
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| 关 键 词： | 径向基函数 无网格配置法 自由参数 |
A Meshless Method for Elliptic Equations by Collation with Radial Basis Functions |
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| Institution: | XIANG Juan,Qin Xinqiang,XU Tingting, DANG Faning( 1. College of Science, Xi＇an University of Technology, Xi＇an 710048 ; 2. Institute of Water Resources and Hydropower, Xi＇an University of Technology, Xi＇an 710048 ) |
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| Abstract: | A meshless method for one and two-dimensional elliptic equations by collation with radial basis functions was structured, and the existence of only solution was given, at the same time, the relations of the solution precision and the free parameter c in the radial basis functions were obtained. The formulas for the optimum value of free parameter and its calculated value when the nodes were uniformly distributed were also obtained from the solution. We applied those formulas to the condition of random nodes and found its solution could still keep a satisfied precise,which meant that this method wasn＇t sensitive to the distribution of nodes. |
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| Keywords: | radial basis function meshless method by collation free parameter |
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