Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation

Ömer Yapman and Gabil M. Amiraliyev

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: A linear Volterra delay-integro-differential equation with a singular perturbation parameter ε is considered. The problem is discretized using exponentially fitted schemes on the Shishkin type meshes. It is proved that the numerical approximations generated by this method are O(N−2lnN) convergent in the discrete maximum norm, where N is the mesh parameter. Numerical results show a good agreement with the theoretical analysis.

Keywords: Volterra delay-integro-differential equation; Singular perturbation; Finite difference method; Uniform convergence (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004549

DOI: 10.1016/j.chaos.2021.111100

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