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 new class of high-order time-marching schemes with dissipationuser-control and unconditional stability for parabolic equations. High-ordertime integrators can deliver the optimal performance of highly-accurate androbust spatial discretizations such as isogeometric analysis. Thegeneralized-$\alpha$ method delivers unconditional stability and second-orderaccuracy in time and controls the numerical dissipation in the discretespectrum's high-frequency region. Our goal is to extend the generalized-$alpha$methodology to obtain a high-order time marching methods with high accuracy anddissipation in the discrete high-frequency range. Furthermore, we maintain thestability region of the original, second-order generalized-$alpha$ method foethe new higher-order methods. That is, we increase the accuracy of thegeneralized-$\alpha$ method while keeping the unconditional stability anduser-control features on the high-frequency numerical dissipation. Themethodology solve $k>1, k\in \mathbb{N}$ matrix problems and updates the systemunknowns, which correspond to higher-order terms in Taylor expansions to obtain$(3/2k)^{th}$-order method for even $k$ and $(3/2k+1/2)^{th}$-order for odd$k$. A single parameter $\rho^\infty$ controls the dissipation, and the updateprocedure follows the formulation of the original second-order method.Additionally, we show that our method is A-stable and setting $\rho^\infty=0$allows us to obtain an L-stable method. Lastly, we extend this strategy toanalyze the accuracy order of a generic method.

Higher-order generalized-$\alpha$ methods for parabolic problems