Blatov, Igor; Kitaeva, Elena; Zadorin, Nikita Cubic spline on a Bakhvalov mesh in the presence of a boundary layer. (English) Zbl 1520.65010 Badriev, Ildar B. (ed.) et al., Mesh methods for boundary-value problems and applications. 13th international conference, Kazan, Russia, October 20–25, 2020. Cham: Springer. Lect. Notes Comput. Sci. Eng. 141, 39-55 (2022). MSC: 65D07 PDFBibTeX XMLCite \textit{I. Blatov} et al., Lect. Notes Comput. Sci. Eng. 141, 39--55 (2022; Zbl 1520.65010) Full Text: DOI
Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V. Application of cubic splines on Bakhvalov meshes in the case of a boundary layer. (English. Russian original) Zbl 1480.65036 Comput. Math. Math. Phys. 61, No. 12, 1911-1930 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 12, 1955-1973 (2021). MSC: 65D07 65L11 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Comput. Math. Math. Phys. 61, No. 12, 1911--1930 (2021; Zbl 1480.65036); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 12, 1955--1973 (2021) Full Text: DOI
Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V. Approximation of a function and its derivatives on the basis of cubic spline interpolation in the presence of a boundary layer. (English. Russian original) Zbl 1416.65053 Comput. Math. Math. Phys. 59, No. 3, 343-354 (2019); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 3, 367-379 (2019). MSC: 65D07 41A15 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Comput. Math. Math. Phys. 59, No. 3, 343--354 (2019; Zbl 1416.65053); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 3, 367--379 (2019) Full Text: DOI
Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V. On the parameter-uniform convergence of exponential spline interpolation in the presence of a boundary layer. (English. Russian original) Zbl 06909573 Comput. Math. Math. Phys. 58, No. 3, 348-363 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 3, 365-382 (2018). MSC: 65-XX 41-XX PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Comput. Math. Math. Phys. 58, No. 3, 348--363 (2018; Zbl 06909573); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 3, 365--382 (2018) Full Text: DOI
Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V. Parabolic spline interpolation for functions with large gradient in the boundary layer. (English. Russian original) Zbl 1379.41007 Sib. Math. J. 58, No. 4, 578-590 (2017); translation from Sib. Mat. Zh. 58, No. 4, 745-760 (2017). Reviewer: V. Leontiev (Ul’yanovsk) MSC: 41A15 65D07 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Sib. Math. J. 58, No. 4, 578--590 (2017; Zbl 1379.41007); translation from Sib. Mat. Zh. 58, No. 4, 745--760 (2017) Full Text: DOI
Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V. Cubic spline interpolation of functions with high gradients in boundary layers. (English. Russian original) Zbl 1369.41008 Comput. Math. Math. Phys. 57, No. 1, 7-25 (2017); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 1, 9-28 (2017). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A15 41A25 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Comput. Math. Math. Phys. 57, No. 1, 7--25 (2017; Zbl 1369.41008); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 1, 9--28 (2017) Full Text: DOI
Blatov, I. A.; Dobrobog, N. V.; Kitaeva, E. V. Conditional \(\epsilon\)-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems. (English. Russian original) Zbl 1366.65074 Comput. Math. Math. Phys. 56, No. 7, 1293-1304 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 7, 1323-1334 (2016). Reviewer: Srinivasan Natesan (Assam) MSC: 65L11 65L10 65L60 65L50 34B05 34E15 65L20 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Comput. Math. Math. Phys. 56, No. 7, 1293--1304 (2016; Zbl 1366.65074); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 7, 1323--1334 (2016) Full Text: DOI
Blatov, Igor A.; Blatova, Victoria V.; Rozhec, Yurii B.; Strygin, Vadim V. Galerkin-Petrov method for strongly nonlinear singularly perturbed boundary value problems on special meshes. (English) Zbl 0887.65089 Appl. Numer. Math. 25, No. 4, 321-332 (1997). Reviewer: N.Parhi (Berhampur) MSC: 65L10 34B15 65L60 65L70 34E15 65L50 PDFBibTeX XMLCite \textit{I. A. Blatov} et al., Appl. Numer. Math. 25, No. 4, 321--332 (1997; Zbl 0887.65089) Full Text: DOI