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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 4, Pages 698–710 (Mi zvmmf11963)

Papers published in the English version of the journal

Finite difference method for advanced Volterra integro-differential equation with delay

H. Acara, I. Amiralib, M. E. Durmazc, G. M. Amiraliyevd

a Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Istanbul Kent University, 34433, Istanbul, Türkiye
b Department of Mathematics, Faculty of Arts and Sciences, Düzce University, 81620, Düzce, Türkiye
c Digital Transformation Office, Kırklareli University, 39100, Kırklareli, Türkiye
d Paşa Neighborhood, Şişli District, 34377, Istanbul, Türkiye

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.

Key words: advanced Volterra integro-differential equation with delay, finite difference scheme, uniform convergence, error estimate.

Received: 24.02.2024
Revised: 19.12.2024
Accepted: 04.02.2025

Language: English


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:4, 698–710


© Steklov Math. Inst. of RAS, 2025