ON THE VOLTERRA DELAY-INTEGRO-DIFFERENTIAL EQUATION WITH LAYER BEHAVIOR AND ITS NUMERICAL SOLUTION

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Amiraliyev G., Yapman Ö.

MISKOLC MATHEMATICAL NOTES, cilt.20, ss.75-87, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.2424
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.75-87
  • Anahtar Kelimeler: Volterra delay-integro-differential equation, singular perturbation, finite difference, uniform convergence, LINEAR MULTISTEP METHODS, INTEGRODIFFERENTIAL EQUATIONS, STABILITY
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented.