| Author Name | Affiliation | | Fuzhang Wang | School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, Jiangsu, China
School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China | | Congcong Li | Department of Mathematics, University of Macau, Macau 999078, China | | Kehong Zheng | College of Water Conservancy and Ecological Engineering, Nanchang Institute of Technology, Nanchang 330099, China |
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| Abstract: |
| The radial basis functions (RBFs) play an important role in the numerical simulation processes of partial differential equations. Since the radial basis functions are meshless algorithms, its approximation is easy to implement and mathematically simple. In this paper, the commonly-used multiquadric RBF, conical RBF, and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable coefficients. Numerical results were provided to show the good performance of the three RBFs as numerical tools for a wide range of problems. It is shown that the conical RBF numerical results were more stable than the other two radial basis functions. From the comparison of three commonly-used RBFs, one may obtain the best numerical solutions for boundary value problems. |
| Key words: radial basis functions partial differential equations variable coefficient |
| DOI：10.11916/j.issn.1005-9113.2020025 |
| Clc Number:O242; O29 |
| Fund: |
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| Descriptions in Chinese: |
| 径向基函数求解变系数偏微分方程的比较研究 王福章1,2，李丛丛3，郑克红4 （1. 徐州工程学院 数学与统计学院，徐州 221018； 2. 淮北师范大学 数学科学学院， 淮北 235000； 3. 澳门大学 数学系， 澳门 999078，中国 4. 南昌工程学院 水利与生态工程学院， 南昌 330099） 摘要：径向基函数在数值模拟偏微分方程过程中起着重要作用。由于径向基函数不需要网格划分，因此径向基函数是求解各种类型偏微分方程的一个非常强大的工具。本文利用三种常用径向基函数：Multiquadric、圆锥(Conical)和高斯(Gaussian)径向基函数，求解变系数偏微分方程。数值结果表明，这三种径向基函数对于许多问题都的求解具有较好的数值模拟结果。此外，圆锥径向基函数比其余两个径向基函数具有更稳定的数值模拟结果。通过比较三种常用的径向基函数，可以获得最佳的求解精度。 关键词：径向基函数，偏微分方程，变系数 |
