Name
Title | ||
|---|---|---|
High-Dimensional Nonlinear Ginzburg-Landau Equation With Fractional Laplacian: Discretization And Simulations |
Abstract | ||
|---|---|---|
Y In this paper, we propose a three-level linearized finite difference scheme for the high-dimensional nonlinear Ginzburg-Landau equation with fractional Laplacian. The Crank-Nicolson scheme is used for time discretization, and the fractional Laplacian is discretized by the fractional centered difference scheme. The proposed difference scheme (i.e. a linear system) can be solved efficiently by fast Fourier transform (FFT) and complex conjugate gradient method, since the coefficient matrix is a multi-level block Toeplitz matrix. Furthermore, we analyze the unique solvability and boundedness of solution of the difference scheme by the discrete energy method. It is also proved that the difference scheme is unconditionally stable and second-order accurate in time and space with respect to l(infinity)-norm. Finally, several numerical examples are provided to validate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.cnsns.2021.105920 | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION |
Keywords | DocType | Volume |
nonlinear Ginzburg-Landau equation, Fractional Laplacian, Unique solvability, Convergence, Error estimate in maximum norm | Journal | 102 |
ISSN | Citations | PageRank |
1007-5704 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rui Du | 1 | 0 | 0.68 |
| Yanyan Wang | 2 | 21 | 8.87 |
| Zhaopeng Hao | 3 | 0 | 1.35 |