difference schemes for a singular perturbed problems, problems in unbounded domains, .spline-interpolation in a boundary layer, quadrature formulas for functions with large gradients, formulas of numerical differentiation
Main publications:
Zadorin A. I., Raznostnye skhemy dlya nelineinykh differentsialnykh uravnenii s malym parametrom v ogranichennykh i neogranichennykh oblastyakh, Dissertatsiya na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk, IVMiMG SO RAN, Novosibirsk, 2000 , 320 pp. http://elibrary.ru/item.asp?id=19150456
Zadorin A.I., KONEChNO-RAZNOSTNYE METODY REShENIYa URAVNENII S MALYM PARAMETROM, dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk / Nauch. ruk. Viktor Nikolaevich Ignatev, VTs SO AN SSSR, Novosibirsk, 1985 , 132 pp.
A. I. Zadorin, “Formulas for numerical differentiation on a uniform mesh in the presence of a boundary layer”, Comput. Math. Math. Phys., 64:6 (2024), 1167–1175
2.
A. I. Zadorin, “Analysis of numerical differentiation formulas on a uniform grid in the presence of a boundary layer”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 4, 2024, 106–116
3.
A. I. Zadorin, “Formuly chislennogo differentsirovaniya na ravnomernoi setke pri nalichii pogranichnogo sloya”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 64:6 (2024), 922–931
4.
A .I. Zadorin, “Approximation of a function by polynomials in the presence of a region of large gradients”, Sibirskie elektronnye matematicheskie izvestiya, 21:2 (2024), 1108–1117
5.
A. I. Zadorin, “Primenenie formuly Teilora dlya priblizheniya mnogochlenami funktsii dvukh peremennykh s bolshimi gradientami”, Matematicheskie trudy, 27:4 (2024), 81–92
6.
A. I. Zadorin, S B. Shagaev, “Dvukhsetochnyi metod na setke Bakhvalova dlya ellipticheskoi singulyarno vozmuschennoi zadachi”, Matematicheskie struktury i modelirovanie, 2024, no. 4 (72), 63–72
2023
7.
A.I. Zadorin“. Formulas for Numerical Differentiation of Functions with Large Gradients”, Numerical Analysis and Applications, 16:1 (2023), 14–21
8.
A.I. Zadorin, “Analysis of Numerical Differential Formulas on a Bakhvalov Mesh
in the Presence of a Boundary Layer”, Computational Mathematics and Mathematical Physics, 63:2 (2023), 175–183
9.
A. I. Zadorin, “Application of a Taylor series to approximate a function with large gradients”, Sibirskie elektronnye matematicheskie izvestiya, 20:2 (2023), 1420–1429;
2022
10.
I.A. Blatov, A.I. Zadorin, “Analysis of approaches to spline interpolation of functions with large gradients in the boundary layer”, Journal of Physics: Conference Series, 2182 (2022), 012016 , 11 pp.
11.
A.I. Zadorin, “Approaches to constructing two-dimensional interpolation formulas in the presence of boundary layers”, Journal of Physics: Conference Series, 2182 (2022), 012036 , 9 pp.
A.I.Zadorin, N.A. Zadorin, “Lagrange Interpolation and the Newton–Cotes Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer”, Computational Mathematics and Mathematical Physics, 62:3 (2022). 347–358
13.
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, (39):2 (2022), 142–149
14.
A.I. Zadorin,, “Two-dimensional interpolation of functions with large gradients
in boundary layers.”, Sibirskie elektronnye matematicheskie izvestiya, 19:2 (2022), 688–697
15.
A.I. Zadorin, “Two-dimensional interpolation of functions by cubic splines in the presence of boundary layers”, Journal of Mathematical Sciences, 267:4 (2022), 511–518
A.I. Zadorin, “Interpolation of functions with large gradients in the boundary layer”, Sovremennoe sostoyanie i perspektivy razvitiya tsifrovykh tekhnologii i iskusstvennogo intellekta v upravlenii, sbornik dokladov respublikanskoi nauchno-tekhnicheskoi konferentsii “Sovremennoe sostoyanie i perspektivy razvitiya tsifrovykh tekhnologii i iskusstvennogo intellekta v upravlenii” (Samarkand, 26-27 oktyabrya 2022 goda.), 2, Tashkent: Izd-vo NII RTsTII,, 2022, 136–141
2021
17.
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
18.
I.A., Blatov, A.I. Zadorin“. Application a cubic spline to calculate derivatives in the presence of a boundary layer”, Journal of Physics: Conference Series, 1791 (2021), 012069 , 8 pp.
A.I. Zadorin, “New approaches to constructing quadrature formulas for functions with large gradients”, Journal of Physics: Conference Series, 1901:1 (2021), 012055 , 10 pp.
20.
I.A. Blatov, A.I. Zadorin , E.V. Kitaeva, “Application of Cubic Splines on Bakhvalov Meshes in the Case of a Boundary Layer”, Computational Mathematics and Mathematical Physics, 61:12 (2021), 1911–1930
21.
A.I. Zadorin, “Otsenka pogreshnosti dvumernoi splain-interpolyatsii pri nalichii pogranichnykh sloev”, Prikladnaya matematika i fundamentalnaya informatika, 8:4 (2021), 4–9
2020
22.
I.A. Blatov, A.I. Zadorin , E.V. Kitaeva, “Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers”, Computational Mathematics and Mathematical Physics, 60:3 (2020), 411–426
23.
A.I. Zadorin, “Optimization of nodes of Newton-Cotes formulas in the presence of an exponential boundary layer”, Journal of Physics: Conference Series, 1546 (2020), 012107 , 8 pp.
24.
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, 2020, 2642, eds. Sergei S. Goncharov, Yuri G. Evtushenko, CEUR Workshop Proceedings, 2020, 1-7www./~ceur-ws.org/Vol-2642 zadorin/paper7.pdf
25.
A.I. Zadorin“. Reduction of a boundary value problem for a system of diffusion-reaction equations to problem for a finite interval // Journal of Physics: Conference Series, 2020, v. 1441, 012178.”, Journal of Physics: Conference Series, 1441 (2020), 012178 , 9 pp.
2019
26.
Alexander Zadorin, Igor Blatov, “Analogue of Cubic Spline for Functions with Large Gradients in a Boundary Layer”, Lecture Notes in Computer Science, 11386, eds. I. Dimov, L. Vulkov, Springer, 2019, 654–662
27.
I.A. Blatov , A.I. Zadorin , E.V. Kitaeva, “Approximation of a Function and Its Derivatives on the Basis
of Cubic Spline Interpolation in the Presence of a Boundary Layer”, Computational Mathematics and Mathematical Physics, 59:3 (2019), 343–354
28.
A. Zadorin, S. Tikhovskaya, “Formulas of numerical differentiation on a uniform mesh for functions with the exponential boundary layer”, International Journal of Numerical Analysis and Modeling, 16:4 (2019), 590-608www.math.ualberta.ca/ijnam/Volume-16-2019/No-4-19/2019-04-04.pdf
29.
I.A. Blatov , A.I. Zadorin, “Approaches to the calculation of derivatives of functions with large gradients in the boundary layer under the values at the grid nodes”, Journal of Physics: Conference Series, 1158:1 (2019), 022029 , 6 pp.
30.
I.A. Blatov, A.I. Zadorin, E.V. Kitaeva, “An application of the cubic spline on Shishkin mesh for the approximation of a function and its derivatives in the presence of a boundary layer”, Journal of Physics: Conference Series, 1210 (2019), 012017 , 8 pp.
31.
V.P. Il’in, A.I. Zadorin, “Adaptive formulas of numerical differentiation of functions with large gradients Journal of Physics: Conference Series”, Journal of Physics: Conference Series, 1260 (2019), 042003 , 7 pp.
I.A. Blatov, N.V, Dobrobog, A.I. Zadorin, Metody splain-funktsii dlya zadach s pogranichnym sloem, Povolzhskii gosudarstvennyi universitet telekommunikatsii i informatiki, Samara, 2019 , 258 pp.
33.
.Zadorin A.I., Ilin V.P., “Adaptivnye formuly chislennogo differentsirovaniya pri nalichii pogranichnogo sloya”, Trudy Mezhdunarodnoi konferentsii " Aktualnye problemy vychislitelnoi i prikladnoi matematiki”. (Novosibirsk, IVM i MG SO RAN, 1 – 5 iyulya 2019 g.,), izd–vo IVM i MG SO RAN,, 2019, 144–150
2018
34.
I.A. Blatov , A.I. Zadorin , E.V. Kitaeva, “On the Parameter–Uniform Convergence of Exponential Spline Interpolation in the Presence of a Boundary Layer”, Computational Mathematics and Mathematical Physics, 58:3 (2018), 348–363
35.
I.A. Blatov , A.I. Zadorin , E.V. Kitaeva, “An application of the exponential spline for the approximation of a function and its derivatives in the presence of a boundary layer”, Journal of Physics: Conference Series, 1050:1 (2018), 012012 , 7 pp.
36.
A.I. Zadorin, “Analysis of Numerical Differentiation Formulas in a Boundary Layer on a Shishkin Grid”, Numerical Analysis and Applications, 11:3 (2018), 193–203
37.
Blatov I.A., Zadorin A.I., Kitaeva E.V., “Approksimatsiya proizvodnykh funktsii s bolshimi gradientami na osnove splainovoi interpolyatsii”, Trudy Mezhdunarodnoi konferentsii "Vychislitelnaya matematika i matematicheskaya geofizika”, posvyaschennoi 90-letiyu so dnya rozhdeniya akademika A.S. Alekseeva. (Novosibirsk, IVM i MG SO RAN, 8 – 12 oktyabrya 2018 g.,), izd–vo IVM i MG SO RAN,, Novosibirsk, 2018, 60–66
2017
38.
I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Cubic spline interpolation of functions with high gradients in boundary layers”, Comput. Math. Math. Phys., 57:1 (2017), 7–25
39.
A. Zadorin, “Two-Dimensional Interpolation of Functions with Large Gradients in Boundary Layers”, Lecture Notes in Computer Science, 10187, eds. I. Dimov, L. Vulkov, Springer, 2017, 760–768
40.
I. A. Blatov, E. V. Kitaeva , A. I. Zadorin, “On the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Numerical Analysis and Applications, 10:2 (2017), 108–119
41.
I. A. Blatov , A. I. Zadorin, E. V. Kitaeva, “Parabolic spline interpolation for functions with large gradient in the boundary layer”, Siberian Mathematical Journal, 58:4 (2017), 578–590
42.
A. I. Zadorin, “Kubaturnye formuly dlya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Sibirskie elektronnye matematicheskie izvestiya, 14 (2017), 927–936
43.
A. I. Zadorin, “Splain-interpolyatsiya pri nalichii pogranichnogo sloya”, Informatsionnyi byulleten Omskogo nauchno-obrazovatelnogo tsentra OmGTU i IM SO RAN v oblasti matematiki i informatiki, 1, eds. A.V. Zykina, OmGTU, Omsk, 2017, 35–38
44.
I.A. Blatov, A.I. Zadorin, E.V. Kitaeva, “Ob interpolirovanii L-splainami funktsii s bolshimi gradientami v pogranichnom sloe”, Trudy Mezhdunarodnoi konferentsii po vychislitelnoi i prikladnoi matematike “VPM’17” v ramkakh “Marchukovskikh nauchnykh chtenii”, (Novosibirsk, 25 iyunya – 14 iyulya 2017 g.), IVM i MG SO RAN, Novosibirsk, 2017, 100-105http://conf.nsc.ru/cam17/ru/proceedings
45.
S.V. Tikhovskaya, A.I. Zadorin, “Formuly chislennogo differentsirovaniya funktsii s bolshimi gradientami”, Trudy Mezhdunarodnoi konferentsii po vychislitelnoi i prikladnoi matematike "VPM’17 v ramkakh "Marchukovskikh nauchnykh chtenii (Novosibirsk, 25 iyunya – 14 iyulya 2017 g.), IVM i MG SO RAN, Novosibirsk, 2017, 878–884http://conf.nsc.ru/cam17/ru/proceedings
2016
46.
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
47.
Zadorin, A.I., “Gauss quadrature on a piecewise uniform mesh for functions with large gradients in a boundary layer”, Siberian Electronic Mathematical Reports, 13:1 (2016), 101-110
48.
A. I. Zadorin, “Interpolation formulas for functions with large gradients in the boundary layer and their application”, Model. i analiz inform. sistem, 23:3 (2016), 377–384
Zadorin, A.I., Zadorin, N. A., “Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component”, COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 56:3 (2016), 358-366http://link.springer.com/article/10.1134
50.
S. V. Tikhovskaya , A. I. Zadorin, “Analysis of polynomial interpolation of the function of two variables with large gradients in the parabolic boundary layers”, Eighth International Conference on Application of Mathematics in Technical and Natural Sciences (Albena, Bulgaria, 22.06 – 27.06.2016), AIP Conference Proceedings, 1773, eds. Todorov, MD, AIP Publishing LLC, 2016, 100008-1–100008-9
Blatov I. A., Kitaeva E. V., Zadorin A. I., “On interpolation by cubic splines of the functions with a boundary layers”, CEUR Workshop Proceedings, 1638 (2016), 515-520
52.
A. I. Zadorin, “Interpolyatsionnye formuly dlya funktsii s bolshimi gradientami v pogranichnykh sloyakh”, Prikladnaya matematika i fundamentalnaya informatika, 3 (2016), 11–15
53.
A. I. Zadorin, “Dvumernye interpolyatsionnye formuly dlya funktsii s bolshimi gradientami v pogranichnykh sloyakh”, Setochnye metody dlya kraevykh zadach i prilozheniya. Materialy Odinnadtsatoi Mezhdunarodnoi konferentsii., Kazanskii (Privolzhskii) federalnyi universitet, Kazan, 2016, 133–138
2015
54.
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
Zadorin, A.I., “Interpolation of a function of two variables with large gradients in boundary layers”, Lobachevskii Journal of Mathematics, 37:3 (2016), 349-359http://link.springer.com/article/10.1134
2015
56.
A.I. Zadorin, “Lagrange interpolation and Newton-Cotes formulas for functions with boundary layer components on piecewise-uniform grids”, Numerical Analysis and Applications, 8:3 (2015), 235-247
57.
A. Zadorin, “The Analysis of Lagrange Interpolation for Functions with a Boundary Layer Component”, Lecture Notes in Computer Science, 9045, Springer, 2015, 426–432
S.V. Tikhovskaya , A. I. Zadorin, “A two-grid method with Richardson extrapolation for a semilinear convection-diffusion problem”, Seventh Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (Albena, BULGARIA Date: JUN 28.06 – 03.07 2015), AIP Conference Proceedings, 1684, eds. Todorov, MD, American Institute of Physics, 2015, 090007
A. I. Zadorin, N. A. Zadorin, “Simpson rule and its modifications for a function with a boundary layer component”, Siberian Elektronic Mathematical Reports, 11 (2014), 258–267
60.
Zadorin A.I., “Modification of the Euler Quadrature Formula for Functions with a Boundary-Layer Component”, Computational Mathematics and Mathematical Physics, 54:10 (2014), 1489-1498
61.
A. I. Zadorin, “Analog kubicheskogo splaina dlya interpolyatsii funktsii s pogransloinoi sostavlyayuschei”, Setochnye metody dlya kraevykh zadach i prilozheniya. Materialy Desyatoi Mezhdunarodnoi konferentsii, Kazanskii (Privolzhskii) federalnyi universitet, Kazan, 2014, 305–310
2013
62.
A. I. Zadorin, S. V . Tikhovskaya, “Solving a Second-Order Nonlinear Singular Perturbation Ordinary Differential Equation by a Samarskii Scheme”, Numerical Analysis and Applications, 6:1 (2013), 9–23
63.
A. I. Zadorin, S. V. Tikhovskaya, “A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin scheme”, Sib. Zh. Ind. Mat., 16:1 (2013), 42–55
64.
A. I. Zadorin, N. A. Zadorin, “Euler quadrature rule for a function with a boundary layer component on a picewise uniform mesh”, Siberian Elektronic Mathematical Reports, 10 (2013), 491–503
65.
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), 268–278http://link.springer.com/article/10.1134
66.
A. Zadorin. N. Zadorin, “Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component”, Lecture Notes in Computer Science, 8236, Springer, 2013, 540– 546
A. I. Zadorin, N. A. Zadorin, “Interpolyatsiya funktsii s uchetom pogranichnogo sloya i ee primeneniya”, Setochnye metody dlya kraevykh zadach i prilozheniya. Materialy Devyatoi Vserossiiskoi konferentsii, eds. otv. redaktor I. B. Badriev; sost. V. V. Banderov., Otechestvo, Kazan, 2012, 147–151
2011
70.
Zadorin, A.I. , Zadorin, N.A., “Interpolation of functions with the boundary layer components and its application in a two-grid method”, Siberian Electronic Mathematical Reports, 8:1 (2011), 247-267
71.
A. I. Zadorin, S. V. Tikhovskaya, “Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids”, Num. Anal. Appl., 4:1 (2011), 36–45
72.
A.I. Zadorin, “Spline interpolation of functions with a boundary layer component”, International Journal of Numerical Analysis & Modeling - Series B, 2:2-3 (2011), 262-279
73.
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
2013
74.
Zadorin, A.I. , Tikhovskaya, S.V., “Difference Scheme on a Uniform Grid for the Singularly Perturbed Cauchy Problem”, Journal of Mathematical Sciences (United States), 195:6 (2013), 865-872
2011
75.
A. I. Zadorin , M. V. Guryanova, “Analogue of a Cubic Spline for a Function with a Boundary Layer Component”, Proceedings of the Fifth Conference on Finite Difference Methods: Theory and Applications, 2010, Rousse University, Rousse, Bulgaria, 2011, 166–173
2010
76.
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
77.
L.G. Vulkov, A.I. Zadorin, “Two-Grid Algorithms for an ordinary second order equation with exponential boundary layer in the solution”, International Journal of Numerical Analysis and Modeling, 7:3 (2010), 580-592
2009
78.
L.G. Vulkov, A.I. Zadorin, “Two-Grid Algorithms for the Solution of 2D Semilinear Singularly Perturbed Convection-Diffusion Equations Using an Exponential Finite Difference Scheme”, Conference: 1st International Conference on Application of Mathematics in Technical and Natural Sciences, Euro Amer Consortium Promoting Applicat Math Tech & Nat Sci APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (Sozopol, BULGARIA Date: JUN 22-27 2009), AIP Conference Proceedings, 1186, eds. Todorov, MD; Christov, CI, American Institute of Physics, 2009, 371-379
L.G. Vulkov, A.I. Zadorin, “A Two-Grid Algorithm for Solution of the Difference Equations of a System of Singular Perturbed Semilinear Equations // Lect. Notes in Computer Science, 2009, v. 5434, Springer-Verlag, Berlin, p. 580-587.”, Lecture Notes in Computer Science, 5434, Springer, 2009, 580-587
A. I. Zadorin, “Refined-mesh interpolation method for functions with a boundary-layer component”, Comput. Math. Math. Phys., 48:9 (2008), 1634–1645
82.
L.G. Vulkov, A.I. Zadorin, “Two-grid Interpolation Algorithms for Difference Schemes of Exponential Type for Semilinear Diffusion Convection-Dominated Equations”, Conference Proceedings, 1067, American Institute of Physics, 2008, 284-292
A.I. Zadorin, A.V. Chekanov, “Numerical Method for Three-Point Vector Difference Schemes on Infinite Interval”, International Journal of Numerical Analysis and Modeling, 5:2 (2008), 190-206
84.
A. I. Zadorin, “Metod interpolyatsii dlya funktsii dvukh peremennykh s pogransloinoi sostavlyayuschei”, Vychislitelnye tekhnologii, 13:3 (2008), 45-53
A. I. Zadorin, “Method of interpolation for a boundary layer problem”, Sib. Zh. Vychisl. Mat., 10:3 (2007), 267–275
2006
88.
A. I. Zadorin, “Numerical Method for Blasius Equation on an infinite Interval”, Proceedings of an International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Minisymposium Robust Numerical Methods for Problems with Layer Phenomena and Applications, Georg-August University Gottingen, 2006, 1–7 \href{www.num.math.uni-goettingen.de/bail/documents/proceedings/zadorin.pdf}
2005
89.
A.I. Zadorin , O.V. Kharina, “Numerical Method for a Chemical Nonlinear Reaction Boundary Value Problem”, Lecture Notes in Computer Science, 3401, Springer, 2005, 583-589
2004
90.
A. I. Zadorin, O. V. Kharina, “Numerical method for a system of linear equations of second order with a small parameter on a semi-infinite interval”, Sib. Zh. Vychisl. Mat., 7:2 (2004), 103–114
91.
A.I. Zadorin , O.V. Kharina, “Chislennyi metod dlya nelineinogo uravneniya s pogranichnym sloem, sootvetstvuyuschim zone khimicheskoi reaktsii”, Vychislitelnye tekhnologii, 9:spetsialnyi vypusk, chast2 (2004), 215-221
92.
A. V. Chekanov , A. I. Zadorin, “Numerical method for a singular perturbed elliptic equation in a strip // Proceedings of an International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, ONERA, Toulouse, 2004, Session 5, p. 1-6.”, An international Conference on Boundary And International Layers - Computational&Asymptotic Methods (Toulouse, 5–9 July 2004), ONERA, Toulouse, 2004, 1–6
2003
93.
A. I Zadorin , A. V. Chekanov, “Reduktsiya vektornoi trekhtochechnoi skhemy na beskonechnom intervale k skheme s konechnym chislom uzlov”, Vychislitelnye tekhnologii, 8:3 (2003), 54-70
A.I. Zadorin, Metod vydeleniya mnogoobrazii dlya kraevykh zadach na beskonechnom intervale. // Uchebnoe posobie, Izdatelstvo Omskogo gosudarstvennogo universiteta, Omsk, 2003 , 73 pp.
2002
96.
A. I. Zadorin, A. V. Chekanov, “Reduction of a three-point difference scheme on the infinite interval to a scheme with a finite number of grid nodes”, Sib. Zh. Vychisl. Mat., 5:2 (2002), 149–161
97.
A.I. Zadorin, “Chislennyi metod dlya parabolicheskogo uravneniya s malym parametrom na polubeskonechnom intervale”, Vychislitelnye tekhnologii, 7:spetsialnyi vypusk (2002), 9-16
98.
A. I. Zadorin, “A method of lines for an elliptic problem with boundary layers along a strip”, The International Conference on Computational Mathematics Proceedings: Part 2 (Novosibirsk, 24–28 June 2002), eds. Gennadi A. Mikhailov, Valeri P. Il'in, Yuri M. Laevsky, IGM&MG Publisher, Novosibirsk, 2002, 728–732.
99.
O. V. Harina , A. I. Zadorin, “Numerical solution of a boundary value problem for a system of equations with a small parameter on a half-infinite interval”, The International Conference on Computational Mathematics Proceedings: Part 2 (Novosibirsk, 24–28 June 2002), ICM&MG Publisher, Novosibirsk, 2002, 449-453
100.
A. I. Zadorin, “A second order scheme for nonlinear singularly perturbed two-point boundary value problem”, Differential equations and mathematical modelling, Nova Sci. Publ, Huntington, 2002, 189–196
A. I. Zadorin, “Reduction from a semi-infinite interval to a finite interval of a nonlinear boundary value problem for a system of second-order equations with a small parameter”, Siberian Math. J., 42:5 (2001), 884–892
103.
J.D. Kandilarov , L.G. Vulkov , A.I. Zadorin, “A method of lines approach to the numerical solution of singularly perturbed elliptic problems”, Lecture Notes in Computer Science, 1988, Springer, 2001, 451-458
O. V. elichko, A. I. Zadorin, “Numerical solution of a system of equations with a small parameter and a point source on an infinite interval”, Mathematical structures and modeling, 2001, no. 7, 17–27
106.
A.I. Zadorin, D.N. Lavrov , O.V. Chervyakov, Izdatelskaya sistema LATEX 2e dlya khimikov. // Uchebno-metodicheskoe posobie, Izdatelstvo Omskogo gosudarstvennogo universiteta, 2001 , 100 pp.
2000
107.
A. I. Zadorin, “Reduction of a boundary value problem for a second-order linear vector difference equation to a finite number of grid points”, Comput. Math. Math. Phys., 40:4 (2000), 519–528
Zadorin, AI, “Numerical solution of the nonlinear differential equation with a small parameter on the infinite interval”, ANALYTICAL AND NUMERICAL METHODS FOR CONVECTION-DOMINATED AND SINGULARLY PERTURBED PROBLEMS, Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems (LOZENETZ, BULGARIA Date: AUG 27-31, 1998), ISBN: 1-56072-848-5, eds. Vulkov, LG; Miller, JJH; Shishkin, GI, NOVA SCIENCE PUBLISHERS,, INC, 400 OSER AVE, STE 1600, HAUPPAUGE, NY 11788-3635 USA, 2000, 259-264
110.
Zadorin A. I., Raznostnye skhemy dlya nelineinykh differentsialnykh uravnenii s malym parametrom v ogranichennykh i neogranichennykh oblastyakh, Avtoreferat dissertatsii na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk, Izdatelstvo IVM i MG SO RAN, Novosibirsk, 2000
111.
Zadorin A. I., Raznostnye skhemy dlya nelineinykh differentsialnykh uravnenii s malym parametrom v ogranichennykh i neogranichennykh oblastyakh, Dissertatsiya na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk, IVMiMG SO RAN, Novosibirsk, 2000 , 320 pp. http://elibrary.ru/item.asp?id=19150456
112.
A. I. Zadorin, “A difference scheme for a problem with a power boundary layer”, Mathematical structures and modeling, 2000, no. 6, 36–42
113.
A. I. Zadorin, “A difference scheme for an elliptic equation with a power boundary layer in a strip”, Mathematical structures and modeling, 2000, no. 5, 11–17
114.
O. V. Velichko, A. I. Zadorin, “Numerical solution of an equation with a point source on an infinite interval”, Mathematical structures and modeling, 2000, no. 5, 5–10
1999
115.
A. I. Zadorin, “The transfer of the boundary condition from the infinity for the numerical solution to the second order equations with a small parameter”, Sib. Zh. Vychisl. Mat., 2:1 (1999), 21–35
116.
A.I Zadorin, “Chislennoe reshenie ellipticheskogo uravneniya s pogranichnymi sloyami v polubeskonechnoi polose”, Vychislitelnye tekhnologii, 4:1 (1999), 33-47
1998
117.
A. I. Zadorin, “Numerical solution of the equation with a small parameter and a point source on the infinite interval”, Sib. Zh. Vychisl. Mat., 1:3 (1998), 249–260
118.
A. I. Zadorin, “Numerical solution of an equation with a small parameter on an infinite interval”, Comput. Math. Math. Phys., 38:10 (1998), 1602–1614
119.
A. I. Zadorin, “Numerical solution of a boundary value problem for a set of equations with a small parameter”, Comput. Math. Math. Phys., 38:8 (1998), 1201–1211
120.
A. I. Zadorin, “Transfer of a boundary condition from infinity in the case of a second-order linear equation with a small parameter”, Mathematical structures and modeling, 1998, no. 1, 13–19
A. I. Zadorin, “Numerical solution of a nonlinear ordinary equation with a boundary layer that corresponds to the reaction zone. (Russian)”, Fundamental and applied mathematics, Omsk. Gos. Univ., Omsk, 1994, 107–111
1993
123.
A. I. Zadorin, “Chislennoe reshenie ellipticheskogo uravneniya s parabolicheskim pogransloem”, Modelirovanie v mekhanike, 7:1 (1993), 52–59
1991
124.
A. I. Zadorin, V. N. Ignat'ev, “Numerical solution of a quasilinear second-order singularly perturbed equation”, Computational Mathematics and Mathematical Physics, 31:1 (1991), 112–116
125.
A.I. Zadorin, “Chislennoe reshenie obyknovennogo uravneniya vtorogo poryadka so slabo vyrazhennym pogranichnym sloem”, Modelirovanie v mekhanike, 5:1, ITPM SO AN SSSR, 1991, 141-152
1990
126.
ZADORIN, AI (ZADORIN, AI); IGNATYEV, VN (IGNATYEV, VN),, “A DIFFERENCE SCHEME FOR A NONLINEAR SINGULARLY PERTURBED 2ND-ORDER EQUATION”, USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 30:5 (1990), 107-111
127.
A. I. Zadorin, Raznostnaya skhema dlya obyknovennogo singulyarno vozmuschennogo uravneniya vtorogo poryadka, Preprint№899, VTs SO AN SSSR, VTs SO AN SSSR, Novosibirsk, 1990 , 18 pp.
1989
128.
A.I. Zadorin, “Raznostnaya skhema dlya samosopryazhennoi singulyarno vozmuschennoi tretei kraevoi zadachi”, Modelirovanie v mekhanike, 3:1, ITPM SO AN SSSR, 1989, 77-82
129.
A.I. Zadorin, “Zadorin A.I.Chislennoe reshenie kvazilineinogo uravneniya s malym parametrom. // Modelirovanie v mekhanike, 1989,t.3, N 2, c. 89-94.”, Modelirovanie v mekhanike, 3:2, ITPM SO AN SSSR, 1989, 89-94
1986
130.
ZADORIN, AI; IGNATEV, VN, “NUMERICAL-SOLUTION OF THE SINGULAR PERTURBATION 3RD BOUNDARY-PROBLEM FOR THE GENERAL EQUATION OF THE 2ND-ORDER”, IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1986, no. 11, 20-26
131.
V.N. Ignat'ev , A.I. Zadorin, “finite-difference method for calculation of a two-dimensional laminar flame”, Combustion, Explosion and Shock waves, 22:4 (1986), 423-425
132.
A.I. Zadorin, “7. Zadorin A.I.Chislennoe reshenie kvazilineinogo singulyarno vozmuschennogo uravneniya. // Chislennye metody mekhaniki sploshnoi sredy, Novosibirsk, 1986, t.17, # 6, c. 35-44.”, Chislennye metody mekhaniki sploshnoi sredy, 17:6, ITPM SO AN SSSR, 1986, 35-44
133.
V. N. Ignatev , A. I. Zadorin, O nekotorykh metodakh chislennogo resheniya nelineinoi singulyarno- vozmuschennoi kraevoi zadachi. // Preprint VTs SO AN SSSR, Novosibirsk, 1986, # 677., Preprint №677, VTs SO AN SSSR, VTs SO AN SSSR, Novosibirsk, 1986 (to appear) , 28 pp.
1985
134.
Zadorin A.I., KONEChNO-RAZNOSTNYE METODY REShENIYa URAVNENII S MALYM PARAMETROM, dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk / Nauch. ruk. Viktor Nikolaevich Ignatev, VTs SO AN SSSR, Novosibirsk, 1985 , 132 pp.
1984
135.
ZADORIN, AI, “NUMERICAL-SOLUTION OF THE 3RD BOUNDARY-VALUE PROBLEM FOR AN EQUATION WITH A SMALL PARAMETER”, USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 24:4 (1984), 28-33
136.
A.I. Zadorin, “O suschestvovanii i edinstvennosti resheniya nekotorykh raznostnykh zadach dlya kvazilineinogo obyknovennogo differentsialnogo uravneniya s malym parametrom”, Chislennye metody mekhaniki sploshnoi sredy, 15:1, ITPM SO AN SSSR, 1984, 33-44
1983
137.
A.I. Zadorin, “O vydelenii pogranichnogo sloya i sochetanii nachalnykh i kraevykh zadach pri reshenii singulyarno vozmuschennykh uravnenii”, Chislennye metody mekhaniki sploshnoi sredy, 14:1, ITPM SO AN SSSR, 1983, 42-50
138.
ZADORIN, AI; IGNATEV, VN, “ON THE NUMERICAL-SOLUTION OF EQUATIONS WITH A SMALL PARAMETER IN THE HIGHEST DERIVATIVE”, USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 23:3 (1983), 10.1016/S0041-5553(83)80103-7 , 66-71 pp.
V. N. Ignatev , A. I. Zadorin, “Regulyarizatsiya raznostnykh skhem s pomoschyu pervogo differentsialnogo priblizheniya pri chislennom reshenii uravnenii s malym parametrom pri starshei proizvodnoi”, Chislennye metody i zadachi optimizatsii, Tomsk, TGU, 1982, 5–11
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