Finite Difference Method for Advanced Volterra Integro-Differential Equation with Delay

Acar H., Amirali I., Durmaz M., Amiraliyev G.

Computational Mathematics and Mathematical Physics, cilt.65, sa.4, ss.698-710, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 4
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1134/s0965542525700149
  • Dergi Adı: Computational Mathematics and Mathematical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, INSPEC, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.698-710
  • Anahtar Kelimeler: advanced Volterra integro-differential equation with delay, error estimate, finite difference scheme, uniform convergence
  • İstanbul Kent Üniversitesi Adresli: Evet

Özet

Abstract: The aim of this paper is to introduce a numerical method for advanced Volterra delay integro-differential equation with initial condition. A finite difference scheme on a uniform mesh using the trapezoidal formula is developed to numerically solve this problem. Additionally, demonstrated that this approach yields second-order convergence in the discrete maximum norm. The proposed method is validated through the presentation of numerical results.