A backward Euler difference scheme for the integro-differential equations with the multi-term kernels

Abstract

ABSTRACTA backward Euler difference scheme is formulated and analyzed for the integro-differential equations with the multi-term kernels. The convolution quadrature is used to deal with the Riemann-Liouville fractional integral terms. A fully discrete difference scheme is constructed with time derivative by backward Euler scheme and space discretization by standard central difference approximation. We prove the stability and convergence based on the nonnegative character of the real quadratic form. The and -norms stability and convergence are given. Finally, numerical experiments validate the theoretical results.