Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation
发布时间：2020-09-01
点击次数：
影响因子：3.37
DOI码：10.1016/j.camwa.2020.05.027
发表刊物：Computers and Mathematics with Applications
关键字：Space-fractional Ginzburg–Landau equation; BDF2 method; Compact finite difference scheme; ADI
摘要：Space and time approximations for two-dimensional space fractional complex Ginzburg–Landau equation are examined. The schemes under consideration are discreted by the second-order backward differential formula (BDF2) in time and two classes of the fractional centered finite difference methods in space. A linearized technique is employed by the extrapolation. We prove the unique solvability and stability for both numerical methods. The convergence of both numerical methods is analyzed at length utilizing the energy argument, and the convergence orders under the optimal step size ratio are O(τ 2 + h2) and O(τ 2 + h4) in the sense of the discrete L2-norm, where τ is the time step size, h = max{hx, hy}, and hx, hy are spatial grid sizes in the x-direction and y-direction, respectively. In addition, we construct a multistep alternating direction implicit (ADI) scheme and a multistep compact ADI scheme based on BDF2 for the efficiently numerical implementation. Finally, numerical examples are carried out to verify our theoretical results.
合写作者：Xiaoman Lin, Kejia Pan, Yunzhu Ren
第一作者：Qifeng Zhang
论文类型：期刊论文
通讯作者：Qifeng Zhang
文献类型：J
卷号：80
期号：5
页面范围：1201–1220
是否译文：否
发表时间：2020-09-01
收录刊物：SCI
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