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


Amirali I., Dağ D., Durmaz M. E., Amiraliyev G. M.

Boundary Value Problems, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1186/s13661-026-02259-z
  • Dergi Adı: Boundary Value Problems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: Neutral Volterra integro-differential equation, Finite difference scheme, Uniform convergence, Error analysis
  • Kırklareli Üniversitesi Adresli: Evet

Özet

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.