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

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  • Yapman, Ömer
  • Amiraliyev, Gabil M.

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.

Suggested Citation

  • Yapman, Ömer & Amiraliyev, Gabil M., 2021. "Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004549
    DOI: 10.1016/j.chaos.2021.111100
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    References listed on IDEAS

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    1. Wu, Shifeng & Gan, Siqing, 2009. "Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3148-3159.
    2. Angelina Bijura, 2002. "Singularly perturbed Volterra integral equations with weakly singular kernels," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-15, January.
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