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

In this paper, we develop a novel class of linear energy-preservingintegrating factor methods for the 2D nonlinear Schr\"odinger equation withwave operator (NLSW), combining the scalar auxiliary variable approach and theintegrating factor methods. A second-order scheme is first proposed, which isrigorously proved to be energy-preserving. By using the energy methods, weanalyze its optimal convergence in the $H^1$ norm without any restrictions onthe grid ratio, where a novel technique and an improved induction argument areproposed to overcome the difficulty posed by the unavailability of a priori$L^\infty$ estimates of numerical solutions. Based on the integrating factorRunge-Kutta methods, we extend the proposed scheme to arbitrarily high order,which is also linear and conservative. Numerical experiments are presented toconfirm the theoretical analysis and demonstrate the advantages of the proposedmethods.

Linearly implicit energy-preserving integrating factor methods for the  2D nonlinear Schr\"odinger equation with wave operator and convergence  analysis