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, a Semi-Lagrangian Runge-Kutta method is proposed to com-pute the numerical solution of time-dependent partial di®erential equations.The method is based on Lagrangian trajectory or the integration from the de-parture points to the arrival points (regular nodes). The departure points aretraced back from the arrival points along the trajectory of the path. The highorder interpolation is needed to compute the approximations of the solutionson the departure points, which most likely are not the regular nodes. On thetrajectory of the path, the similar techniques of Runge-Kutta are applied to theequations to generate the high order Semi-Lagrangian Runge-Kutta method.The numerical examples show that this method works very effient for thetime-dependent partial di®erential equations.

A SEMI-LAGRANGIAN RUNGE-KUTTA METHOD FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS