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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Stability and convergence of a time-weighted discrete scheme with nonuniformtime steps are established for linear reaction-subdiffusion equations. TheCaupto derivative is approximated at an offset point by using linear andquadratic polynomial interpolation. Our analysis relies on two tools: adiscrete fractional Gr\"{o}nwall inequality and the global consistencyanalysis. The new consistency analysis makes use of an interpolation errorformula for quadratic polynomials, which leads to a convolution-type bound forthe local truncation error. To exploit these two tools, some theoreticalproperties of the discrete kernels in the numerical Caputo formula are crucialand we investigate them intensively in the nonuniform setting. Taking theinitial singularity of the solution into account, we obtain a sharp errorestimate on nonuniform time meshes. The fully discrete scheme generates asecond-order accurate solution on the graded mesh provided a proper gradingparameter is employed. An example is presented to show the sharpness of ouranalysis.

A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problem