Alternating direction implicit difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel. (15th January 2020)

• Record Type: Journal Article
• Authors: Zhou, Jun; Xu, Da
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 2(2020)
• Page Start: 244
• Page End: 255
• Publication Date: 2020-01-15
• Subjects: Multi-term time-fractional -- Integro-differential equation -- Weakly singular kernel -- Alternating direction implicit difference scheme -- Convergence -- Numerical experiments; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.06.027
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present an alternating direction implicit (ADI) difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel. The Caputo fractional derivative is discretized by L1 method and the integro-differential term is discretized by a convolution quadrature suggested by Lubich. The stability and optimal convergence order estimate of the difference scheme are derived. Numerical experiments verify our theory analysis.