The difference schemes for solving singularly perturbed three-point boundary value problem
LITHUANIAN MATHEMATICAL JOURNAL, cilt.60, sa.2, ss.147-160, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 60 Sayı: 2
- Basım Tarihi: 2020
- Doi Numarası: 10.1007/s10986-020-09471-z
- Dergi Adı: LITHUANIAN MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, DIALNET
- Sayfa Sayıları: ss.147-160
- Anahtar Kelimeler: boundary value problem, exponentially fitted difference scheme, nonlocal condition, singular perturbation, uniformly convergence
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
In this paper, we propose and analyze numerical treatment for a singularly perturbed convection-diffusion boundary value problem with nonlocal condition. First, the boundary layer behavior of the exact solution and its first derivative have been estimated. Then we construct a finite difference scheme on a uniform mesh. We prove the uniform convergence of the proposed difference scheme and give an error estimate. We also present numerical examples, which demonstrate computational efficiency of the proposed method.