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<p>In this study, a second-order numerical method is proposed for solving a third-order neutral type Volterra integro-differential equation (NVIDE). The proposed method is based on finite difference approximations for the differential terms and a suitable quadrature rule for the integral term. The method is constructed on a uniform mesh and is shown to achieve second-order accuracy. Stability and convergence analyses are carried out under appropriate assumptions. A numerical experiment is presented to verify the efficiency, accuracy, and theoretical order of convergence of the proposed scheme.</p>

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A second-order numerical method to the third order neutral Volterra integro-differential equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月9日

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  • Ilhame Amirali,
  • Damla Dağ,
  • Muhammet Enes Durmaz,
  • Gabil M. Amiraliyev

摘要

In this study, a second-order numerical method is proposed for solving a third-order neutral type Volterra integro-differential equation (NVIDE). The proposed method is based on finite difference approximations for the differential terms and a suitable quadrature rule for the integral term. The method is constructed on a uniform mesh and is shown to achieve second-order accuracy. Stability and convergence analyses are carried out under appropriate assumptions. A numerical experiment is presented to verify the efficiency, accuracy, and theoretical order of convergence of the proposed scheme.