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/

Zendy Plus

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

Zendy Tools

Zendy Open

High order strong stability preserving (SSP) time discretizations are oftenneeded to ensure the nonlinear (and sometimes non-inner-product) strongstability properties of spatial discretizations specially designed for thesolution of hyperbolic PDEs. Multiderivative time-stepping methods haverecently been increasingly used for evolving hyperbolic PDEs, and the strongstability properties of these methods are of interest. In our prior work weexplored time discretizations that preserve the strong stability properties ofspatial discretizations coupled with forward Euler and a second derivativeformulation. However, many spatial discretizations do not satisfy strongstability properties when coupled with this second derivative formulation, butrather with a more natural Taylor series formulation. In this work wedemonstrate sufficient conditions for an explicit two-derivative multistagemethod to preserve the strong stability properties of spatial discretizationsin a forward Euler and Taylor series formulation. We call these strongstability preserving Taylor series (SSP-TS) methods. We also prove that themaximal order of SSP-TS methods is p = 6, and define an optimization procedurethat allows us to find such SSP methods. Several types of these methods arepresented and their efficiency compared. Finally, these methods are tested onseveral PDEs to demonstrate the benefit of SSP-TS methods, the need for the SSPproperty, and the sharpness of the SSP time-step in many cases.

A Strong Stability Preserving Analysis for Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions