Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay

Yapman Ö., Amiraliyev G. M., Amirali I.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.355, ss.301-309, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 355
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.cam.2019.01.026
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.301-309
  • Anahtar Kelimeler: Finite difference method, Volterra delay-integro-differential equation, Singular perturbation, Uniform convergence, LINEAR MULTISTEP METHODS, DIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, KERNEL
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.