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On the second-order neutral Volterra integro-differential equation and its numerical solution

Author

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  • Amirali, Ilhame
  • Fedakar, Burcu
  • Amiraliyev, Gabil M.

Abstract

In this paper, we consider an initial-value problem for a second-order neutral Volterra integro-differential equation. First, we give the stability inequality indicating the stability of the problem with respect to the right-side and initial conditions. Further, we develop a finite difference method that uses for differential part second difference derivative, for the integral part appropriate composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points. Error estimate for the approximate solution is established, which shows the second-order accuracy. Finally, the numerical experiments are presented confirming the accuracy of the proposed scheme.

Suggested Citation

  • Amirali, Ilhame & Fedakar, Burcu & Amiraliyev, Gabil M., 2024. "On the second-order neutral Volterra integro-differential equation and its numerical solution," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    • Handle: RePEc:eee:apmaco:v:476:y:2024:i:c:s0096300324002339
    DOI: 10.1016/j.amc.2024.128765
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