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A three‐level linearized compact difference scheme for the Ginzburg–Landau equation
Author(s) -
Hao ZhaoPeng,
Sun ZhiZhong,
Cao WanRong
Publication year - 2015
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.21925
Subject(s) - mathematics , partial differential equation , norm (philosophy) , scheme (mathematics) , mathematical analysis , order (exchange) , first order , differential equation , law , finance , political science , economics
A high‐order finite difference method for the two‐dimensional complex Ginzburg–Landau equation is considered. It is proved that the proposed difference scheme is uniquely solvable and unconditionally convergent. The convergent order in maximum norm is two in temporal direction and four in spatial direction. In addition, an efficient alternating direction implicit scheme is proposed. Some numerical examples are given to confirm the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 876–899, 2015