Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation
Bulletin of the Belgian Mathematical Society - Simon Stevin, cilt.27, sa.1, ss.71-88, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 27 Sayı: 1
- Basım Tarihi: 2020
- Doi Numarası: 10.36045/bbms/1590199305
- Dergi Adı: Bulletin of the Belgian Mathematical Society - Simon Stevin
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.71-88
- Anahtar Kelimeler: Finite differencemethods, Fredholm integro-differential equation, Shishkin mesh, Singular perturbation, Uniform convergence
- Kırklareli Üniversitesi Adresli: Evet
Özet
In this paper, we consider the linear first order singularly perturbed Fredholm integro-differential equation. For the solution of this problem, fitted difference scheme is constructed on a Shishkinmesh. Themethod 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 method is proved to be second-order convergent in the discrete maximum norm. Also, numerical results are given to support theoretical analysis.