Methods of spline-interpolation for boundary layer problems and its applications.
Main publications:
A.I. Zadorin , N.A. Zadorin, “Spline Interpolation on a Uniform Grid for Functions with a Boundary-Layer Component”, Computational Mathematics and Mathematical Physics, 50:2 (2010), 211–223
A.I. Zadorin, N.A. Zadorin, “Quadrature formulas for functions with a boundary-layer component”, Computational Mathematics and Mathematical Physics, 51:11 (2011), 1837–1846
A. I. Zadorin, N. A. Zadorin, “Spline interpolation on a uniform grid for a function with a boundary layer component”, Comput. Math. Math. Phys., 50:2 (2010), 211–223
2.
A. I. Zadorin, N. A. Zadorin, “Quadrature formulas for functions with a boundary-layer component”, Comput. Math. Math. Phys., 51:11 (2011), 1837–1846
3.
A. I. Zadorin, N. A. Zadorin, “Interpolation formula for functions with a boundary layer component and its application to derivatives calculation”, Sib. elektron. matem. izv., 9 (2012), 445–455
2. A. I. Zadorin , S. V. Tikhovskaya, N. A. Zadorin, “A two-grid method for elliptic problem with boundary layers”, Applied Numerical Mathematics, 93 (2015), 270-278
A. I. Zadorin, N. A. Zadorin, “An analogue of Newton–Cotes formula with four nodes for a function with a boundary-layer component”, Num. Anal. Appl., 6:4 (2013), 268–278
6.
A.I. Zadorin, N.A. Zadorin“. Non-Polynomial Interpolation of Functions with Large Gradients and Its Application”, Computational Mathematics and Mathematical Physics, 61:2 (2021), 167–176
7.
A. I. Zadorin, N. A. Zadorin, “Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component”, Comput. Math. Math. Phys., 56:3 (2016), 358–366
8.
A. I. Zadorin, N. A. Zadorin, “Interpolation of functions with the boundary layer components and its application in a two-grid method”, Sib. Èlektron. Mat. Izv., 8 (2011), 247–267
A. I. Zadorin, N. A. Zadorin, “Lagrange interpolation and the Newton–Cotes formulas on a Bakhvalov mesh in the presence of a boundary layer”, Comput. Math. Math. Phys., 62:2 (2022), 347–358
11.
A. I. Zadorin, N. A. Zadorin, “Polynomial interpolation of the function of two variables with large gradients in the boundary layers”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158:1 (2016), 40–50
12.
A. Zadorin, N. Zadorin, “Quadrature formula with five nodes for functions with a boundary layer component”, Lecture notes in computer science, 8236 (2013), 540–546
A. I. Zadorin, N. A. Zadorin, “Euler quadrature rule for a function with a boundary layer component on a picewise uniform mesh”, Sib. Èlektron. Mat. Izv., 10 (2013), 491–503
15.
A. I. Zadorin, N. A. Zadorin, “Simpson rule and its modifications for a function with a boundary layer component”, Sib. Èlektron. Mat. Izv., 11 (2014), 258–267
16.
A.I. Zadorin, N.A. Zadorin, “Application of the two-grid method for solving a singularly perturbed elliptic problem”, Problems of Computational and Applied Mathematics ., 2022, no. 2(39), 142–149
17.
N.A. Zadorin, S.B. Shagaev, “Dvukhsetochnyi metod na setke Bakhvalova dlya ellipticheskoi singulyarno vozmuschennoi zadachi”, Problemy mashinovedeniya.
Materialy VI Mezhdunarodnoi nauchno-tekhnicheskoi konferentsii. Omsk, 2022
Izdatelstvo: Omskii gosudarstvennyi tekhnicheskii universitet (Omsk) (OMGTU, Omsk, 22-23 marta 2022), OMGTU, Omsk, 2022, 165–170
18.
I. Blatov, E. Kitaeva, N. Zadorin, “Cubic Spline on a Bakhvalov Mesh in the Presence of a Boundary Layer.”, Lecture Notes in Computational Science and Engineering, 141, Springer, Cham. (2022), 39-55https://link.springer.com/chapter/10.1007/978-3-030-87809-2_4
19.
N.A, Zadorin, S.B. Shagaev, “Two-grid method for the stationary Burgers equation”, Journal of Physics: Conference Series, 1791 (2021), 012090 , 7 pp.
A. Zadorin, N. Zadorin, “The spline approach to the calculation of derivatives on the Bakhvalov mesh in the presence of a boundary layer.”, Proceedings of the Workshop on Applied Mathematics and Fundamental Computer Science 2020, Omsk, Russia, April 23-30 ., 2642, eds. Sergei S. Goncharov, Yuri G. Evtushenko, CEUR Workshop Proceedings, 2020, 1–7www.ceur-ws.org/Vol-2642/~zadorin/paper7.pdf
22.
N. A. Zadorin, “Interpolyatsionnye i kvadraturnye formuly dlya funktsii s pogransloinoi sostavlyayuschei na setke Shishkina”, Vestnik Omskogo universiteta, 2012, no. 4, 17–20
23.
N. A. Zadorin, “Optimization of nodes of composite quadrature formulas in the presence of a boundary layer”, Sib. elektron. matem. izv., 18:2 (2021), 1201–1209;
24.
N. A. Zadorin, “Analysis of formulas for numerical differentiation of functions with large gradients on a Bakhvalov mesh”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 163, no. 3, Kazan University, Kazan, 2021, 261–275
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