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On convergence and performance of iterative methods with fourth‐order compact schemes
Author(s) -
Zhang Jun
Publication year - 1998
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(199803)14:2<263::aid-num8>3.0.co;2-m
Subject(s) - spectral radius , mathematics , discretization , convergence (economics) , iterative method , partial differential equation , matrix (chemical analysis) , reduction (mathematics) , fourier analysis , partial derivative , fourier transform , mathematical analysis , mathematical optimization , eigenvalues and eigenvectors , geometry , economics , economic growth , physics , materials science , quantum mechanics , composite material
We study the convergence and performance of iterative methods with the fourth‐order compact discretization schemes for the one‐ and two‐dimensional convection–diffusion equations. For the one‐dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two‐dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:263–280, 1998