V. A. Belyaev, A. I. Boltaev, L. S. Bryndin, S. K. Golushko, A. G. Gorynin, V. P. Shapeev, “Modelling and simulation of deformation and failure of reinforced concrete beams under four-point bending”, Zhurn. SFU. Ser. Matem. i fiz., 14:6 (2021), 679–689
V. A. Belyaev, L. S. Bryndin, S. K. Golushko, B. V. Semisalov, V. P. Shapeev, “H-, p- i hp-varianty metoda kollokatsii i naimenshikh kvadratov dlya resheniya kraevykh zadach dlya bigarmonicheskogo uravneniya v neregulyarnykh oblastyakh i ikh prilozheniya”, Zh. vychisl. matem. i matem. fiz., 62:4 (2022), 521-552
B. V. Semisalov, V. A. Belyaev, L. S. Bryndin, A. G. Gorynin, A. M. Blokhin, S. K. Golushko, V. P. Shapeev, “Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section”, Applied Mathematics and Computation, 430 (2022), 127294
L. S. Bryndin, B. V. Semisalov, V. A. Beliaev, V. P. Shapeev, “Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front”, Computational Mathematics and Mathematical Physics, 61:1 (2024), 151-165
2.
L. S. Bryndin, V. A. Belyaev, “Kollokatsionnye metody s polinomami chetvertoi stepeni na treugolnykh setkakh i ikh primenenie dlya rascheta izgiba kruglykh plastin s otverstiyami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 30:1 (2024), 43-60
2023
3.
L. S. Bryndin, V. A. Belyaev, V. P. Shapeev, “Razrabotka i verifikatsiya uproschennogo hp-varianta metoda kollokatsii i naimenshikh kvadratov dlya neregulyarnykh oblastei”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:3 (2023), 35-50
2022
4.
V. P. Shapeev, L. S. Bryndin, V. A. Belyaev, “Numerical solution of an elliptic problem with several interfaces”, Num. Meth. Prog., 23:3 (2022), 172–190
5.
V. P. Shapeev, L. S. Bryndin, V. A. Belyaev, “The hp-version of the least-squares collocation method with integral collocation for solving a biharmonic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:3 (2022), 556–572
6.
V. A. Belyaev, L. S. Bryndin, S. K. Golushko, B. V. Semisalov, V. P. Shapeev, “H-, P-, and HP-versions of the least-squares collocation method for solving boundary value problems for biharmonic equation in irregular domains and their applications”, Comput. Math. Math. Phys., 62:4 (2022), 517–537
7.
B. V. Semisalov, V. A. Belyaev, L. S. Bryndin, A. G. Gorynin, A. M. Blokhin, S. K. Golushko, V. P. Shapeev, “Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section”, Applied Mathematics and Computation, 430 (2022), 127294
Vasily A. Belyaev, Artem I. Boltaev, Luka S. Bryndin, Sergey K. Golushko, Arsenii G. Gorynin, Vasily P. Shapeev, “Modelling and simulation of deformation and failure of reinforced concrete beams under four-point bending”, Zhurn. SFU. Ser. Matem. i fiz., 14:6 (2021), 679–689;
9.
V. A. Belyaev, “On the effective implementation and capabilities of the least-squares collocation method for solving second-order elliptic equations”, Num. Meth. Prog., 22:3 (2021), 211–229
10.
V. P. Shapeev, V. A. Belyaev, L. S. Bryndin, “High accuracy numerical solution of elliptic equations with discontinuous coefficients”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:4 (2021), 88–101;
11.
S. K. Golushko, V. P. Shapeev, V. A. Belyaev, L. S. Bryndin, A. I. Boltaev, A. G. Gorynin, “The least-squares collocation method in the mechanics of deformable solids”, Journal of Physics: Conference Series, 1715, IOP Publishing Ltd, 2021, 012029
12.
V. P. Shapeev, S. K. Golushko, V. A. Belyaev, L. S. Bryndin, P. I. Kirillov, “New versions of the least-squares collocation method for solving differential and integral equations”, Journal of Physics: Conference Series, 1715, IOP Publishing Ltd, 2021, 012031
V. A. Belyaev, “Solving the Poisson equation with singularities by the least-squares collocation method”, Num. Anal. Appl., 13:3 (2020), 207–218
14.
V. A. Belyaev, L. S. Bryndin, V. P. Shapeev, S. K. Golushko, “The least squares collocation method with the integral form of collocation equations for bending analysis of isotropic and orthotropic thin plates”, AIP Conference Proceedings, 2288, AIP Publishing, 2020, 030084
V. P. Shapeev, L. S. Bryndin, V. A. Belyaev, “Solving elliptic equations in polygonal domains by the least squares collocation method”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:3 (2019), 140–152
16.
V. A. Belyaev, L. S. Bryndin, V. P. Shapeev, “A h-version of the least squares collocation method for the biharmonic equation in irregular domains”, Journal of Physics: Conference Series, 1214, IOP Publishing Ltd, 2019, 012011
17.
V. P. Shapeev, S. K. Golushko, L. S. Bryndin, V. A. Belyaev, “The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains”, Journal of Physics: Conference Series, 1268, IOP Publishing Ltd, 2019, 012076
V. A. Belyaev, L. S. Bryndin, V. P. Shapeev, “The least squares collocation method for biharmonic-type equations in the plate theory”, AIP Conference Proceedings, 2125, AIP Publishing, 2019, 030061
19.
V. M. Buznik, S. K. Golushko, E. V. Amelina, V. A. Belyaev, L. S. Bryndin, A. G. Gorynin, V. P. Shapeev, “Determining the law of ice deformation”, Journal of Physics: Conference Series, 1404, IOP Publishing Ltd, 2019, 012010
V. P. Shapeev, V. A. Belyaev, “Solving the biharmonic equation with high order accuracy in irregular domains by the least squares collocation method”, Num. Meth. Prog., 19:4 (2018), 340–355
21.
V. P. Shapeev, V. A. Belyaev, “Solving boundary value problems for partial differential equations in triangular domains by the least squares collocation method”, Num. Meth. Prog., 19:1 (2018), 96–111
22.
V.A. Belyaev, V.P. Shapeev, “Reshenie zadachi Dirikhle dlya uravneniya Puassona metodom kollokatsii i naimenshikh kvadratov v oblasti s diskretno zadannoi granitsei”, Vychislitelnye tekhnologii, 23:3 (2018), 15–30
23.
V. P. Shapeev, V. A. Belyaev, S. K. Golushko, S. V. Idimeshev, “New possibilities and applications of the least squares collocation method”, EPJ Web of Conferences, 173, EDP Sciences, 2018, 01012
V. A. Belyaev, V. P. Shapeev, “Solving the biharmonic equation in irregular domains by the least squares collocation method”, AIP Conference Proceedings, 2027, AIP Publishing, 2018, 030094
V. A. Belyaev, V. P. Shapeev, “Versions of the collocation and least residuals method for solving problems of mathematical physics in the convex quadrangular domains”, Model. Anal. Inform. Sist., 24:5 (2017), 629–648
26.
V.A. Belyaev, V.P. Shapeev, “Varianty metoda kollokatsii i naimenshikh nevyazok dlya resheniya zadach matematicheskoi fiziki v trapetsievidnykh oblastyakh”, Vychislitelnye tekhnologii, 22:4 (2017), 22–42
27.
V. A. Belyaev, V. P. Shapeev, “Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains”, AIP Conference Proceedings, 1893, AIP Publishing, 2017, 030102
V. P. Shapeev, V. A. Belyaev, “Varianty metoda kollokatsii i naimenshikh nevyazok povyshennoi tochnosti v oblasti s krivolineinoi granitsei”, Vychislitelnye tekhnologii, 21:5 (2016), 95–110
2024
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