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Legendre spectral method for solving mixed boundary value problems on rectangle
Author(s) -
Wang Tianjun
Publication year - 2016
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.3827
Subject(s) - rectangle , mathematics , legendre polynomials , sobolev space , boundary value problem , dirichlet distribution , space (punctuation) , spectral method , mathematical analysis , geometry , computer science , operating system
In this paper, we develop a spectral method for mixed inhomogeneous Dirichlet/Neumann/Robin boundary value problems defined on rectangle. Some results on two‐dimensional Legendre approximation in Jacobi‐weighted Sobolev space are established. As examples of applications, spectral schemes are provided for two model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms are proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy and confirm the theoretical analysis well. Copyright © 2016 John Wiley & Sons, Ltd.