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

Authors

  • Xuhong Yu School of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P.R.China
  • Yunge Zhao School of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P.R.China
  • Zhongqing Wang School of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

DOI:

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

Keywords:

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

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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Published

2018-08-16

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Issue

Vol. 51 No. 2 (2018)

Section

Articles

How to Cite

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