A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity

•A balanced space-time Sinc-collocation method for viscoelastic heat.•An effective single exponential Sinc method to deal with the initial singularity.•The error estimate is proved rigorously.•Space-time spectral-order convergence order simultaneously. The purpose of this paper is to investigate a s...

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Veröffentlicht in:Applied mathematics and computation Jg. 457; S. 128192
Hauptverfasser: Yang, Xuehua, Wu, Lijiao, Zhang, Haixiang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.11.2023
Schlagworte:
Error estimation
Exponential convergence
Nonlocal heat problem
Sinc-collocation method
Spectral order accuracy
Weakly singular
Weakly singular
Exponential convergence
Sinc-collocation method
Error estimation
65M70
65M06
Nonlocal heat problem
45K05
65M22
Spectral order accuracy
ISSN:0096-3003
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Zusammenfassung:•A balanced space-time Sinc-collocation method for viscoelastic heat.•An effective single exponential Sinc method to deal with the initial singularity.•The error estimate is proved rigorously.•Space-time spectral-order convergence order simultaneously. The purpose of this paper is to investigate a space-time Sinc-collocation method for solving the fourth-order nonlocal heat model arising in viscoelasticity, which is a class of partial integro-differential equations (PIDEs) whose solution typically exhibits the weak singularities at the initial time. Most of existing approximate methods for solving such kind PIDEs are unbalanced, since most work have used a low order scheme for integrating the temporal variable and a high order numerical framework for discretization of space variables. The current paper contributes to a space-time spectral-order Sinc-collocation method which is balanced in both time and space variables. In order to deal with the initial singularity of solution in the time direction, the Sinc-collocation method with single exponential (SE) transformation is used for the first time, which is an effective method to deal with the singularity of the equation. Also, we fully analyse the error bounds of the method which show the exponential convergence rate in space and time. Meanwhile, we consider several test problems for examining the suggested scheme. The experiment results highlight a good precision of the new Sinc-colloction method and the correctness of the theoretical prediction for this kind nonlocal heat problems.
ISSN:0096-3003
DOI:10.1016/j.amc.2023.128192