High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equation

In this paper, we first construct an appropriate new generating function, and then based on this function, we establish a fourth-order numerical differential formula approximating the Riesz derivative with order γ∈(1,2]. Subsequently, we apply the formula to numerically study the two-dimensional non...

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Vydáno v:Communications in nonlinear science & numerical simulation Ročník 120; s. 107160
Hlavní autoři: Ding, Hengfei, Li, Changpin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2023
Témata:
Error estimate
Fourth-order convergence
Ginzburg–Landau equation
Unconditional stability
Unconditional stability
Ginzburg–Landau equation
Fourth-order convergence
Error estimate
ISSN:1007-5704, 1878-7274
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Shrnutí:In this paper, we first construct an appropriate new generating function, and then based on this function, we establish a fourth-order numerical differential formula approximating the Riesz derivative with order γ∈(1,2]. Subsequently, we apply the formula to numerically study the two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equation and obtain a difference scheme with convergence order Oτ2+hx4+hy4, where τ denotes the time step size, hx and hy denote the space step sizes, respectively. Furthermore, with the help of some newly derived discrete fractional Sobolev embedding inequalities, the unique solvability, the unconditional stability, and the convergence of the constructed numerical algorithm under different norms are proved by using the discrete energy method. Finally, some numerical results are presented to confirm the correctness of the theoretical results and verify the effectiveness of the proposed scheme. •A fourth-order numerical differential formula for the Riesz derivative is constructed.•An efficient high-order difference scheme is proposed.•The basic characteristics of the proposed scheme are analyzed under different norms.•The methodology can be extended to other spatial fractional differential equations.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2023.107160