Diagonalized Gegenbauer rational spectral methods for second- and fourth-order problems on the whole line

被引：3

作者：

Li, Shan ^{[1
]}

Lai, Zhenyan ^{[1
]}

Jin, Lusha ^{[1
]}

Yu, Xuhong ^{[1
]}

机构：

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 151卷

基金：

中国国家自然科学基金;

关键词：

Gegenbauer rational spectral methods; Sobolev orthogonal basis functions; Error analysis; Numerical results; PARTIAL-DIFFERENTIAL-EQUATIONS; GALERKIN METHOD; APPROXIMATION;

D O I：

10.1016/j.apnum.2019.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fully diagonalized Gegenbauer rational spectral methods for solving second- and fourth-order differential equations on the whole line are proposed and analyzed. Some Gegenbauer rational Sobolev 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 Gegenbauer rational series. Optimal error estimates of the fully diagonalized Gegenbauer rational spectral method for second-order problem are obtained. Finally, some numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized methods. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：494 / 516

页数：23

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