A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line

A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line

Year:    2018

Author:    Xuhong Yu, Yunge Zhao, Zhongqing Wang

Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 196–213

Abstract

A diagonalized Legendre rational spectral method for solving second and fourth order differential equations are proposed. Some Fourier-like 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 Fourier series. Numerical results demonstrate the effectiveness of this approach.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v51n2.18.05

Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 196–213

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Legendre rational spectral method Sobolev orthogonal functions elliptic boundary value problems heat equation numerical results.

Author Details

Xuhong Yu

Yunge Zhao

Zhongqing Wang