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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The functional distributions of particle trajectories have wide applications,including the occupation time in half-space, the first passage time, and themaximal displacement, etc. The models discussed in this paper are forcharacterizing the distribution of the functionals of the paths of anomalousdiffusion described by time-space fractional diffusion equation. This paperfocuses on providing effective computation methods for the models. Two kinds oftime stepping schemes are proposed for the fractional substantial derivative.The multiresolution Galerkin method with wavelet B-spline is used for spaceapproximation. Compared with the finite element or spectral polynomial bases,the wavelet B-spline bases have the advantage of keeping the Toeplitz structureof the stiffness matrix, and being easy to generate the matrix elements and toperform preconditioning. The unconditional stability and convergence of theprovided schemes are theoretically proved and numerically verified. Finally, wealso discuss the efficient implementations and some extensions of the schemes,such as the wavelet preconditioning and the non-uniform time discretization.

Multiresolution Galerkin method for solving the functional distribution of anomalous diffusion described by time-space fractional diffusion equation