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.
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.
作者
王金平
庄清渠
WANG Jinping ZHUANG Qingqu(School of Mathematical Sciences, Huaqiao University, Quanzhou 362021 , China)
出处
《华侨大学学报（自然科学版）》
北大核心
2017年第3期435-440,共6页
Journal of Huaqiao University(Natural Science)
基金
国家自然科学基金资助项目(11501224)
华侨大学中青年教师科研提升资助计划(ZQN-PY201)
华侨大学研究生科研创新能力培育计划项目(1400213008)
关键词
五阶常微分方程
Petrov-Galerkin谱元法
基函数
数值实验
fifth-order ordinary differential equation
Petrov-Galerkin spectral-element method
basis func-tions
numerical experiments
