A Crank–Nicolson ADI Galerkin–Legendre spectral method for the two-dimensional Riesz space distributed-order advection–diffusion equation. (15th November 2018)

• Record Type: Journal Article
• Authors: Zhang, Hui; Liu, Fawang; Jiang, Xiaoyun; Zeng, Fanhai; Turner, Ian
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 10(2018)
• Page Start: 2460
• Page End: 2476
• Publication Date: 2018-11-15
• Subjects: Two-dimensional Riesz space distributed-order advection–diffusion equation -- ADI Galerkin–Legendre spectral method -- Gauss quadrature -- Stability and convergence analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.08.042
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In the paper, a Crank–Nicolson alternating direction implicit (ADI) Galerkin–Legendre spectral scheme is presented for the two-dimensional Riesz space distributed-order advection–diffusion equation. The Gauss quadrature has a higher computational accuracy than the mid-point quadrature rule, which is proposed to approximate the distributed order Riesz space derivative so that the considered equation is transformed into a multi-term fractional equation. Moreover, the transformed equation is solved by discretizing in space by the ADI Galerkin–Legendre spectral scheme and in time using the Crank–Nicolson difference method. Stability and convergence analysis are verified for the numerical approximation. A lot of numerical results are demonstrated to justify the theoretical analysis.