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

We propose a Lawson-time-splitting extended Fourier pseudospectral (LTSeFP)method for the numerical integration of the Gross-Pitaevskii equation withtime-dependent potential that is of low regularity in space. For the spatialdiscretization of low regularity potential, we use an extended Fourierpseudospectral (eFP) method, i.e., we compute the discrete Fourier transform ofthe low regularity potential in an extended window. For the temporaldiscretization, to efficiently implement the eFP method for time-dependent lowregularity potential, we combine the standard time-splitting method with aLawson-type exponential integrator to integrate potential and nonlinearitydifferently. The LTSeFP method is both accurate and efficient: it achievesfirst-order convergence in time and optimal-order convergence in space in$L^2$-norm under low regularity potential, while the computational cost iscomparable to the standard time-splitting Fourier pseudospectral method.Theoretically, we also prove such convergence orders for a large class ofspatially low regularity time-dependent potential. Extensive numerical resultsare reported to confirm the error estimates and to demonstrate the superiorityof our method.

A Lawson-time-splitting extended Fourier pseudospectral method for the Gross-Pitaevskii equation with time-dependent low regularity potential