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Volume 51, Issue 2
A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line

Xuhong Yu, Yunge Zhao & Zhongqing Wang

DOI: 10.4208/jms.v51n2.18.05

J. Math. Study, 51 (2018), pp. 196-213.

Published online: 2018-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N35, 41A20, 33C45, 35J25, 35J40, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xhyu@usst.edu.cn (Xuhong Yu)

yunge66@foxmail.com (Yunge Zhao)

zqwang@usst.edu.cn (Zhongqing Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-51-196, author = {Yu , XuhongZhao , Yunge and Wang , Zhongqing}, title = {A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {2}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n2.18.05}, url = {http://global-sci.org/intro/article_detail/jms/12463.html} }
TY - JOUR T1 - A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line AU - Yu , Xuhong AU - Zhao , Yunge AU - Wang , Zhongqing JO - Journal of Mathematical Study VL - 2 SP - 196 EP - 213 PY - 2018 DA - 2018/06 SN - 51 DO - http://doi.org/10.4208/jms.v51n2.18.05 UR - https://global-sci.org/intro/article_detail/jms/12463.html KW - Legendre rational spectral method, Sobolev orthogonal functions, elliptic boundary value problems, heat equation, numerical results. AB -

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.

Yu , XuhongZhao , Yunge and Wang , Zhongqing. (2018). A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line. Journal of Mathematical Study. 51 (2). 196-213. doi:10.4208/jms.v51n2.18.05
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