| 基于径向基逼近的KdV方程的无网格辛算法 |
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| 引用本文： | 张胜良.基于径向基逼近的KdV方程的无网格辛算法[J].应用数学,2021,34(2):457-462. |
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| 作者姓名： | 张胜良 |
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| 作者单位： | 南京林业大学经济管理学院, 江苏 南京 210037 |
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| 基金项目： | 南京林业大学高层次人才启动基金(163060126)。 |
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| 摘 要： | 基于径向基逼近理论,本文为KdV方程构造了一个无网格辛算法.首先借助径向基空间离散Hamilton函数以及Poisson括号,把KdV方程转化成一个有限维的Hamilton系统.然后用辛积分子离散有限维系统,得到辛算法.文章进一步讨论了所构造辛算法的收敛性和误差界.数值例子验证了理论分析.
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| 关 键 词： | 无网格方法 径向基函数 守恒律 辛积分子 KDV方程 |
| 收稿时间： | 2020/6/1 0:00:00 |
Meshless Symplectic Radial Basis Procedure for Solving KdV Equation |
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| ZHANG Shengliang.Meshless Symplectic Radial Basis Procedure for Solving KdV Equation[J].Mathematica Applicata,2021,34(2):457-462. |
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| Authors: | ZHANG Shengliang |
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| Institution: | (College of Economics and Management,Nanjing Forestry University,Nanjing 210037,China) |
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| Abstract: | Based on radial basis function(RBF)theory,this study suggests a meshless symplectic approximation for a class of conservative equations.Specifically,Korteweg-de Vries(KdV)equation is chosen as an illustration.We get a Hamiltonian ODE by discretizing Hamiltonian functional and Poisson bracket with RBF interpolation.Then the symplectic algorithm is derived by integrating the resulting system with Euler-centered scheme.The convergence of the algorithm is discussed.Numerical experiments verify the theoretic results. |
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| Keywords: | Meshless method Radial basis function Conservative law Symplectic integrator KdV equation |
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