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