A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Qiu, Wenlin; Xu, Da; Chen, Hongbin
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 10(2020)
• Page Start: 2055
• Page End: 2073
• Publication Date: 2020-10-02
• Subjects: Integro-differential equations -- second-order BDF scheme -- multi-term kernels -- second-order convolution quadrature rule -- stability and convergence; 45K05 -- 65M06 -- 65M12 -- 65M15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1677896
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this article, a formally second-order backward differentiation formula (BDF) finite difference scheme is presented for the integro-differential equations with the multi-term kernels. In the time direction, the time derivative is approximated by a second-order BDF scheme and the Riemann-Liouville (R-L) fractional integral terms are discretized by the second-order convolution quadrature rule. We construct a fully discrete difference scheme with the space discretization by the standard central difference formula. The L 2 and H 1 -norms stability, and convergence in L 2 -norm are derived by the discrete energy method. In the numerical experiments, the results are consistent with the theoretical analysis.