Premium
Uniform convergence of the legendre spectral method for the Zakharov equations
Author(s) -
Ji Yuanyuan,
Ma Heping
Publication year - 2013
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/num.21716
Subject(s) - mathematics , legendre polynomials , convergence (economics) , mathematical analysis , legendre's equation , legendre function , economics , economic growth
Abstract The Legendre spectral and pseudospectral approximations are proposed for the standard Zakharov equations with initial boundary conditions. Optimal H 1 error estimate of the method is given for both semidiscrete and fully discrete schemes. The uniform convergence for the parameter ε relative to the acoustic speed is proved. Moreover, the multidomain Legendre spectral scheme is also constructed, which can be implemented in parallel. Finally, numerical results in single domain and multidomain verify the high accuracy of the Legendre spectral method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013