Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay. Issue 11 (18th August 2017)

• Record Type: Journal Article
• Authors: Zhang, Qifeng; Ran, Maohua; Xu, Dinghua
• Is Part Of: Applicable analysis. Volume 96:Issue 11(2017)
• Page Start: 1867
• Page End: 1884
• Publication Date: 2017-08-18
• Subjects: Semilinear fractional delay partial differential equation -- compact finite difference scheme -- solvability -- convergence -- stability; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1197914
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In the paper, a linearized compact finite difference scheme is presented for the semilinear fractional delay convection-reaction–diffusion equation. Firstly, the equation is transformed into an equivalent semilinear fractional delay reaction–diffusion equation by using a special transformation. Then, the temporal Caputo derivative is discreted by using approximation and the second-order spatial derivative is approximated by the compact finite difference scheme. The solvability, unconditional stability, and convergence in the sense of - and - norms are proved rigorously. Finally, numerical examples are carried out extensively to support our theoretical analysis.