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Numerical simulation of physical fields by the collocation method. (English. Russian original) Zbl 1515.81233

Russ. Phys. J. 64, No. 12, 2283-2291 (2022); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 64, No. 12, 97-104 (2021).

MSC:

81V55 Molecular physics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35G16 Initial-boundary value problems for linear higher-order PDEs
35G30 Boundary value problems for nonlinear higher-order PDEs
Full Text: DOI

References:

[1] Samarskii, AA, The Theory of Difference Schemes (1989), Moscow: Nauka, Moscow · Zbl 0874.65077
[2] Zenkevich, O.; Morgan, K., Finite Elements and Approximation [Russian translation] (1986), Moscow: Mir, Moscow
[3] Li, ZC; Lu, TT; Hu, HY; Cheng, AH-D, Trefftz and Collocation Methods (2008), Cambridge: WIT Press, Cambridge · Zbl 1140.65005
[4] Piltner, R., Eng. Anal. Bound. Elem., 101, 102-112 (2019) · Zbl 1464.74380 · doi:10.1016/j.enganabound.2018.12.010
[5] Liu, C-S; Wang, F.; Gu, Y., Appl. Math. Lett., 87, 87-92 (2019) · Zbl 1428.65100 · doi:10.1016/j.aml.2018.07.028
[6] E. E. Shcherbakova and S. Yu. Knyazev, in: Proc. XV Int. Sci.-Tech. Conf. “Dynamics of Technical Systems” (DTS-2019), Electronic Edition (2019), p. 050035.
[7] Watson, DW; Karageorghis, A.; Chen, CS, J. Comput. Appl. Math., 363, 53-76 (2020) · Zbl 1418.65188 · doi:10.1016/j.cam.2019.05.027
[8] S. Yu. Knyazev and E. E. Shcherbakova, Russ. Phys. J., 59, No. 10, 1616-1622 (2016). · Zbl 1380.81110
[9] I. S. Berezin and N. P. Zhidkov, Methods of Computing, Vol. 1 [in Russian], Nauka, Moscow (1966).
[10] S. Yu. Knyazev and E. E. Shcherbakova, Russ. Phys. J., 60, No. 7, 1124-1132 (2017). · Zbl 1431.81053
[11] Zaliznyak, VE, Fundamentals of Scientific Computing. Introduction to Numerical Methods for Physicists: A textbook (2002), Moscow: Editorial, Moscow
[12] Polyanin, AD; Zaitsev, VF, Handbook on Nonlinear Equations of Mathematical Physics: Exact Solutions (2002), Moscow: Fizmatlit, Moscow
[13] Plokhotnikov, KE, Math. Models Comput. Simul., 12, 2, 221-231 (2020) · doi:10.1134/S2070048220020106
[14] Hnatich, M.; Khmara, VM; Lazur, VY; Reity, OK, Theor. Math. Phys., 190, 3, 345-358 (2017) · Zbl 1369.81034 · doi:10.1134/S0040577917030047
[15] Z. Flugge, Problems in Quantum Mechanical Engineering, Vol. 1 [Russian translation], Mir, Moscow (1974).
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