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June 2021 Discrete singular convolution for fourth-order multi-term time fractional equation
Xingguo Liu, Xuehua Yang, Haixiang Zhang, Yanling Liu
Tbilisi Math. J. 14(2): 1-16 (June 2021). DOI: 10.32513/tmj/19322008118


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.

Funding Statement

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 (2018M631403).


The authors thank the anonymous reviewers for their constructive comments and suggestions.


Download Citation

Xingguo Liu. Xuehua Yang. Haixiang Zhang. Yanling Liu. "Discrete singular convolution for fourth-order multi-term time fractional equation." Tbilisi Math. J. 14 (2) 1 - 16, June 2021.


Received: 14 May 2020; Accepted: 31 October 2020; Published: June 2021
First available in Project Euclid: 2 July 2021

Digital Object Identifier: 10.32513/tmj/19322008118

Primary: 65N12
Secondary: 35K61, 65N30

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences


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Vol.14 • No. 2 • June 2021
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