A fully discrete scheme on piecewise-equidistant mesh for singularly perturbed delay integro-differential equations

Çakır M., Gunes B.

Quaestiones Mathematicae, cilt.47, sa.9, ss.1913-1933, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 9
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2989/16073606.2024.2343669
  • Dergi Adı: Quaestiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1913-1933
  • Anahtar Kelimeler: Delay differential equation, difference scheme, integro-differential equation, singular perturbation, uniform convergence
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Abstract.: This paper chiefly takes into account the singularly perturbed delay Volterra-Fredholm integro-differential equations by numerically. In this context, firstly, priori estimates are given and a new discretization is constructed on piecewise-equidistant mesh by using interpolating quadrature rules [2] and composite integration formulas. Then, the convergence analysis and stability bounds of the presented method are discussed. Finally, numerical results are demonstrated with two test problems.