An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition


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Durmaz M. E., Amirali I., Amiraliyev G. M.

Journal of Applied Mathematics and Computing, cilt.69, sa.1, ss.505-528, 2023 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s12190-022-01757-4
  • Dergi Adı: Journal of Applied Mathematics and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.505-528
  • Anahtar Kelimeler: Finite difference scheme, Fredholm integro-differential equation, Integral boundary condition, Shishkin mesh, Singular perturbation, Uniform convergence
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Kırklareli Üniversitesi Adresli: Evet

Özet

In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.