Exponential Runge–Kutta Methodfor Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations

UM > Faculty of Science and Technology > DEPARTMENT OF MATHEMATICS

Status	已發表Published
	Exponential Runge–Kutta Methodfor Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations
	Zhang, L.; Zhang, Q.F.; Sun, H. W.
	2020-06-01
Source Publication	JournalofScientiﬁcComputing
ISSN	0885-7474
Pages	UNSP59-UNSP59
Abstract	In this work, we study numerically two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equations. A centered ﬁnite difference method is exploited to discretize the spatial variables and leads to a system of the ordinary differential equation, in which the resulting coefﬁcient matrix is complex symmetric and possesses the block Toeplitz structure. An exponential Runge–Kutta method is employed to solve such a system of the ordinary differential equation. Theoretically, the proposed method is second-order accuracy in space and fourth-order accuracy in time, respectively. In the practical implementation, the product of a block Toeplitz matrix exponential and a vector is calculated by the shift-invert Lanczos method. Meanwhile, the sectorial operator (the coefﬁcient matrix) guarantees the fast approximation by the shift-invert Lanczos method. Numerical experiments are carried out to testify the theoretical results and demonstrate that the proposed method enjoys the excellent computational advantage.
Keyword	Space fractional Ginzburg–Landau equation Toeplitz structure Exponential Runge–Kutta method Matrix exponential Shift-invert Lanczos method
Language	英語English
The Source to Article	PB_Publication
PUB ID	50988
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Sun, H. W.
Recommended Citation GB/T 7714	Zhang, L.,Zhang, Q.F.,Sun, H. W.. Exponential Runge–Kutta Methodfor Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations[J]. JournalofScientiﬁcComputing, 2020, UNSP59-UNSP59.
APA	Zhang, L.., Zhang, Q.F.., & Sun, H. W. (2020). Exponential Runge–Kutta Methodfor Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations. JournalofScientiﬁcComputing, UNSP59-UNSP59.
MLA	Zhang, L.,et al."Exponential Runge–Kutta Methodfor Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations".JournalofScientiﬁcComputing (2020):UNSP59-UNSP59.

Files in This Item:
There are no files associated with this item.

If you have any objections to this item, please fill out the form below and the administrator will contact you as soon as possible.
Content:
Email：	*
Affiliation No.
Verification Code:	Refresh

Any comments and suggestions are welcomed.
Title:	*
Content:
Email：	*
Verification Code:	Refresh