Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis. (15th March 2017)

• Record Type: Journal Article
• Authors: Yang, Yin; Chen, Yanping; Huang, Yunqing; Wei, Huayi
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 6(2017)
• Page Start: 1218
• Page End: 1232
• Publication Date: 2017-03-15
• Subjects: Caputo derivative -- Time-fractional diffusion-wave equation -- Jacobi collocation method -- Convergence analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.08.017
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we consider the numerical solution of the time-fractional diffusion-wave equation. Essentially, the time fractional diffusion-wave equation differs from the standard diffusion-wave equation in the time derivative term. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The convergence of the method is rigorously established. Numerical tests are carried out to confirm the theoretical results.