Affiliation:
1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
Abstract
The block-centered finite-difference method has many advantages, and the time-fractional fourth-order equation is widely used in physics and engineering science. In this paper, we consider variable-coefficient fourth-order parabolic equations of fractional-order time derivatives with Neumann boundary conditions. The fractional-order time derivatives are approximated by L1 interpolation. We propose the block-centered finite-difference scheme for fourth-order parabolic equations with fractional-order time derivatives. We prove the stability of the block-centered finite-difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are provided to verify the effectiveness of the block-centered finite-difference scheme.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis