A NUMERICAL METHOD ON BAKHVALOV SHISHKIN MESH FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH A BOUNDARY LAYER
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.71, sa.1, ss.51-67, 2022 (ESCI)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 71 Sayı: 1
- Basım Tarihi: 2022
- Doi Numarası: 10.31801/cfsuasmas.946910
- Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.51-67
- Anahtar Kelimeler: Singularly perturbed, VIDE, difference schemes, uniform convergence, error estimates, RUNGE-KUTTA METHODS, DIFFERENCE METHOD
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
We construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equation (SPVIDE) on Bakhvalov-Shishkin mesh. For the discretization of the problem, we use the integral identities and deal with the emerging integrals terms with interpolating quadrature rules which also yields remaining terms. The stability bound and the error estimates of the approximate solution are established. Further, we demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N-1) uniformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.