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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 3/2020

01.06.2020

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

verfasst von: Lu Zhang, Qifeng Zhang, Hai-Wei Sun

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2020

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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.
Vorheriger Artikel An Equilibrated a Posteriori Error Estimator for Arbitrary-Order Nédélec Elements for Magnetostatic Problems
Nächster Artikel A Spectral Element Method for Option Pricing Under Regime-Switching with Jumps

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Metadaten
Titel
Exponential Runge–Kutta Method for Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations
verfasst von
Lu Zhang
Qifeng Zhang
Hai-Wei Sun
Publikationsdatum
01.06.2020
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 3/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-020-01240-x

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