A fitted approximate method for a Volterra delay-integro-differential equation with initial layer

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Amiraliyev G., Yapman Ö., Kudu M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.48, ss.1417-1429, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15672/hjms.2018.582
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1417-1429
  • Anahtar Kelimeler: Volterra delay-integro-differential equation, singular perturbation, finite difference, uniform convergence, LINEAR MULTISTEP METHODS, INTEGRODIFFERENTIAL EQUATIONS, NUMERICAL-SOLUTIONS, STABILITY ANALYSIS
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The emphasis is on the convergence of numerical method. It is shown that the method displays uniform convergence in respect to the perturbation parameter. Numerical results are also given.