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 and -norms stability, and convergence in -norm are derived by the discrete energy method. In the numerical experiments, the results are consistent with the theoretical analysis.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Hongbin Chen http://orcid.org/0000-0002-8989-3743