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

A new spectral shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method isdeveloped and analyzed to solve a class of two-dimensional initial-boundary fractional diffusionequations with variable coefficients. The method depends basically on the fact that an expansionin a series of shifted Legendre polynomials PL,n(x)PL,m(y), for the function and its space-fractionalderivatives occurring in the partial fractional differential equation (PFDE), is assumed; the expansioncoefficients are then determined by reducing the PFDE with its boundary and initial conditionsto a system of ordinary differential equations (SODEs) for these coefficients. This system may besolved numerically by using the fourth-order implicit Runge-Kutta (IRK) method. This method,in contrast to common finite-difference and finite-element methods, has the exponential rate ofconvergence for the two spatial discretizations. Numerical examples are presented in the form oftables and graphs to make comparisons with the results obtained by other methods and with theexact solutions more easier

A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation