EFFICIENT LEGENDRE DUAL-PETROV-GALERKIN METHODS FOR ODD-ORDER DIFFERENTIAL EQUATIONS

被引：3

作者：

Li, Shan ^{[1
]}

Yan, Shi-Mi ^{[1
]}

Wang, Zhong-Qing ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Sch Sci, Shanghai 200093, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Dual-Petrov-Galerkin spectral methods; Legendre polynomials; Sobolev bi-orthogonal basis functions; odd-order differential equations; numerical results; GENERALIZED LAGUERRE FUNCTIONS; SPECTRAL METHODS; DIRECT SOLVERS; 2ND-ORDER; 2ND;

D O I：

10.3934/dcdsb.2019239

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Efficient Legendre dual-Petrov-Galerkin methods for solving odd-order differential equations are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier-like series. Numerical results indicate that the suggested methods are extremely accurate and efficient, and suitable for the odd-order equations.

引用

页码：1543 / 1563

页数：21

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