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Reducing the computational requirements of the differential quadrature method
Author(s) -
Chen Wen,
Yu Yongxi,
Wang Xinwei
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199609)12:5<565::aid-num2>3.0.co;2-i
Subject(s) - eigenvalues and eigenvectors , nyström method , mathematics , skew , quadrature (astronomy) , weighting , grid , gauss–jacobi quadrature , matrix (chemical analysis) , differential (mechanical device) , inverse , mathematical analysis , gauss–kronrod quadrature formula , geometry , integral equation , computer science , physics , materials science , quantum mechanics , acoustics , optics , composite material , thermodynamics , telecommunications
This article shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew‐centrosymmetric, if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrices can reduce the computational effort of the DQM for calculations of the inverse, determinant, eigenvectors, and eigenvalues by 75%. This computational advantage is also demonstrated via several numerical examples. © 1996 John Wiley & Sons, Inc.