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.
The work was supported by National Natural Science
Foundation of China (11701168, 11601144), Hunan Provincial Natural Science Foundation of
China (2018JJ3108, 2018JJ3109, 2018JJ4062), Scientific Research Fund of Hunan Provincial
Education Department (18B304, YB2016B033), and China Postdoctoral Science Foundation
The authors thank the anonymous reviewers for their constructive comments and suggestions.
"Discrete singular convolution for fourth-order multi-term time fractional equation." Tbilisi Math. J. 14 (2) 1 - 16, June 2021. https://doi.org/10.32513/tmj/19322008118