四阶特征值问题基于降阶格式的一种有效的Legendre-Galerkin逼近  

An Efficient Legendre-Galerkin Approximation Based on Reduced Order Scheme for Fourth Order Eigenvalue Problems

作　　者：魏涛 

机构地区：[1]贵州师范大学数学科学学院,贵州 贵阳

出　　处：《应用数学进展》2023年第4期1981-1988,共8页Advances in Applied Mathematics

摘　　要：本文提出了四阶特征值问题基于降阶格式的一种有效的Legendre-Galerkin逼近。首先,我们引入了一个辅助函数,将原问题转化为一个二阶混合格式。通过引入一些适当的Sobolev空间,其相应的变分形式被建立,并在解足够光滑条件下证明了其等价性。其次,基于Legendre多项式的正交性质,两组紧凑的基函数被构造,并导出具有稀疏系数矩阵的线性特征系统。最后,我们给出了两个数值例子,数值结果表明了算法的收敛性与高精度。In this paper, an efficient Legendre-Galerkin approximation based on reduced order scheme for fourth order eigenvalue problems is presented. First, we introduce an auxiliary function to trans-form the original problem into a second order mixed format. By introducing some suitable Sobolev Spaces, the corresponding variational form is established, and its equivalence is proved if the solu-tion is sufficiently smooth. Secondly, based on the orthogonal property of Legendre polynomials, two groups of compact basis functions are constructed, and a linear characteristic system with sparse coefficients matrix is derived. Finally, we give two numerical examples, and the numerical results show the convergence and high precision of the algorithm.

关 键 词：四阶特征值问题 降阶格式 Legendre-Galerkin逼近 数值例子 

分 类 号：O17[理学—数学]