Collocation methods for third-kind Volterra integral equations with proportional delays

Huiming Song, Yu Xiao and Minghao Chen

Applied Mathematics and Computation, 2021, vol. 388, issue C

Abstract: In this paper, a class of Volterra delay integral equations (VDIEs) with noncompact operators is approximated by collocation methods. The properties of corresponding operators as well as existence, uniqueness and regularity of exact solution are discussed. The existence and uniqueness of collocation solutions are proved under two special graded meshes. Moreover, we present the convergence conditions and convergence order. Finally, some numerical examples are given to verify the validity of the theoretical orders of convergence.

Keywords: third-kind Volterra integral equations; proportional delays; collocation methods; solvability and convergence; noncompact operators (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304677

DOI: 10.1016/j.amc.2020.125509

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