English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper aims to develop a linearly implicit structure-preserving numericalscheme for the space fractional sine-Gordon equation, which is based on thenewly developed invariant energy quadratization method. First, we reformulatethe equation as a canonical Hamiltonian system by virtue of the variationalderivative of the functional with fractional Laplacian. Then, we utilize thefractional centered difference formula to discrete the equivalent systemderived by the invariant energy quadratization method in space direction, andobtain a conservative semi-discrete scheme. Subsequently, the linearly implicitstructure-preserving method is applied for the resulting semi-discrete systemto arrive at a fully-discrete conservative scheme. The stability, solvabilityand convergence in the maximum norm of the numerical scheme are given.Furthermore, a fast algorithm based on the fast Fourier transformationtechnique is used to reduce the computational complexity in practicalcomputation. Finally, numerical examples are provided to confirm ourtheoretical analysis results.

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach