Discrete L1 remainder stability of first and second order schemes for a Volterra integro-differential equation

Wenlin Qiu, Yanping Chen, Xu Xiao and Xiangcheng Zheng

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 219, issue C, 12-27

Abstract: This work investigates the discrete L1 remainder stability of first and second order schemes for a Volterra integro-differential equation, where the backward Euler and backward difference formula schemes are applied in combination with first and second order convolution quadrature for approximating the integral term, respectively. By Hardy’s inequality and complex analysis techniques to accommodate the singularity of generating functions, we prove the long-time L1 remainder stability of numerical solutions of two schemes, which characterizes the long-time behavior of numerical solutions and indicates the preservation of asymptotically periodic stability of numerical schemes as continuous problems. Numerical experiments are performed to substantiate the theoretical analysis.

Keywords: Volterra integro-differential equation; Long-time behavior; L1 remainder stability; Convolution quadrature (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475423005190
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:219:y:2024:i:c:p:12-27

DOI: 10.1016/j.matcom.2023.12.012

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().