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

This is the second part of study on the optimal convergence rate of theexplicit Euler discretization in time for the convection-diffusion equations[Appl. Math. Lett. \textbf{131} (2022) 108048] which focuses onhigh-dimensional linear/nonlinear cases under Dirichlet or Neumann boundaryconditions. Several new corrected difference schemes are proposed based on theexplicit Euler discretization in temporal derivative and central differencediscretization in spatial derivatives. The priori estimate of the correctedscheme with application to constant convection coefficients is provided atlength by the maximum principle and the optimal convergence rate four is provedwhen the step ratios along each direction equal to $1/6$. The correcteddifference schemes have essentially improved {\rm \textbf{CFL}} condition andthe numerical accuracy comparing with the classical difference schemes.Numerical examples involving two-/three-dimensional linear/nonlinear problemsunder Dirichlet/Neumann boundary conditions such as the Fisher equation, theChafee-Infante equation, the Burgers' equation and classification to name a fewsubstantiate the good properties claimed for the corrected difference scheme.

Optimal convergence rate of the explicit Euler method for convection-diffusion equations II: high dimensional cases