| 五阶常微分方程的Petrov-Galerkin谱元法 |
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| 引用本文： | 王金平,庄清渠.五阶常微分方程的Petrov-Galerkin谱元法[J].华侨大学学报(自然科学版),2017,0(3):435-440. |
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| 作者姓名： | 王金平 庄清渠 |
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| 作者单位： | 华侨大学 数学科学学院, 福建 泉州 362021 |
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| 摘 要： | 通过区间剖分,降低数值逼近多项式的阶数,构造满足试探函数空间和检验函数空间的基函数,使得离散问题所对应的线性系统的系数矩阵是稀疏的,并可以进行有效地求解.数值算例验证了五阶常微分方程的Petrov-Galerkin谱元法的有效性和高精度.
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| 关 键 词： | 五阶常微分方程 Petrov-Galerkin谱元法 基函数 数值实验 |
Petrov-Galerkin Spectral-Element Method for Solving Fifth-Order Ordinary Differential Equations |
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| WANG Jinping,ZHUANG Qingqu.Petrov-Galerkin Spectral-Element Method for Solving Fifth-Order Ordinary Differential Equations[J].Journal of Huaqiao University(Natural Science),2017,0(3):435-440. |
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| Authors: | WANG Jinping ZHUANG Qingqu |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | The polynomial order in the numerical approximation is reduced by partitioning the interval into several subintervals, and appropriate basis functions of the trial and test spaces are constructed. Which leads to a linear system with sparse coefficient matrix. Then, an efficient computational process is introduced to solve the linear system.Numerical experiment results demonstrate the high accuracy and effectiveness to the Petrov-Galerkin spectral-element method. |
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| Keywords: | fifth-order ordinary differential equation Petrov-Galerkin spectral-element method basis functions numerical experiments |
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