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

An improved uniform error bound at $O\left(h^m+\varepsilon^2 \tau^2\right)$is established in $H^{\alpha/2}$-norm for the long-time dynamics of thenonlinear space fractional Klein-Gordon equation (NSFKGE). A second-orderexponential wave integrator (EWI) method is used to semi-discretize NSFKGE intime and the Fourier spectral method in space is applied to derive thefull-discretization scheme. Regularity compensation oscillation (RCO) techniqueis employed to prove the improved uniform error bounds at $O\left(\varepsilon^2\tau^2\right)$ in temporal semi-discretization and $O\left(h^m+\varepsilon^2\tau^2\right)$ in full-discretization up to the long-time $T_{\varepsilon}=T /\varepsilon^2$ ($T>0$ fixed), respectively. Complex NSFKGE and oscillatorycomplex NSFKGE with nonlinear terms of general power exponents are alsodiscussed. Finally, the correctness of the theoretical analysis and theeffectiveness of the method are verified by numerical examples.

Improved uniform error bounds of exponential wave integrator method for  long-time dynamics of the space fractional Klein-Gordon equation with weak  nonlinearity