Discrete singular convolution for fourth-order multi-term time fractional equation

X. G. Liu, X. H. Yang, H. X. Zhang, Y. L. Liu, Y. Liu

This paper studies the fourth-order problem with multi-term time fractional integral operator under simply supported type conditions. We first introduce a novel computational approach, the discrete singular convolution (DSC) algorithm, for analyzing this problem. Detailed discrete formulations and the treatment of simply supported boundary condition are established. We provide some numerical results to demonstrate the validity and applicability of the proposed technique. Comprehensive comparisons are given based on a variety of time increment, grid spacing and wave number. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that the DSC algorithm is an accurate, stable and robust approach for solving the fourth-order integro-differential equation with multi-term time fractional integral operator. 

Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 1-16