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Sobolev orthogonal Legendre rational spectral methods for problems on the half line
Author(s) -
Li Shan,
Li Qiaoling,
Wang Zhongqing
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5865
Subject(s) - legendre polynomials , mathematics , orthogonal functions , sobolev space , legendre function , legendre wavelet , legendre's equation , associated legendre polynomials , mathematical analysis , real line , spectral method , basis function , rational function , fourier series , line (geometry) , orthogonal basis , orthogonal polynomials , wavelet , classical orthogonal polynomials , gegenbauer polynomials , discrete wavelet transform , geometry , wavelet transform , physics , quantum mechanics , artificial intelligence , computer science
Modified Legendre rational spectral methods for solving second‐order differential equations on the half line are proposed. Some Sobolev orthogonal Legendre rational 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 and the spectral accuracy of this approach.