Sofronov, Ivan Truncated transparent boundary conditions for second order hyperbolic systems. (English) Zbl 1370.65062 Appl. Numer. Math. 120, 115-124 (2017). MSC: 65M99 35L51 74B99 PDFBibTeX XMLCite \textit{I. Sofronov}, Appl. Numer. Math. 120, 115--124 (2017; Zbl 1370.65062) Full Text: DOI
Sofronov, I.; Dovgilovich, L. Transparent boundary conditions for the wave equation: high-order approximation and coupling with characteristic NRBCs. (English) Zbl 1352.65267 Kirby, Robert M. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2014. Selected papers from the ICOSAHOM conference, June 23–27, 2014, Salt Lake City, UT, USA. Cham: Springer (ISBN 978-3-319-19799-9/hbk; 978-3-319-19800-2/ebook). Lecture Notes in Computational Science and Engineering 106, 465-473 (2015). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65M06 35L05 65M12 PDFBibTeX XMLCite \textit{I. Sofronov} and \textit{L. Dovgilovich}, Lect. Notes Comput. Sci. Eng. 106, 465--473 (2015; Zbl 1352.65267) Full Text: DOI
Arnold, Anton; Ehrhardt, Matthias; Schulte, Maike; Sofronov, Ivan Discrete transparent boundary conditions for the Schrödinger equation on circular domains. (English) Zbl 1256.35103 Commun. Math. Sci. 10, No. 3, 889-916 (2012). MSC: 35Q41 35A35 65M06 45K05 65M12 PDFBibTeX XMLCite \textit{A. Arnold} et al., Commun. Math. Sci. 10, No. 3, 889--916 (2012; Zbl 1256.35103) Full Text: DOI
Sofronov, I. L. Differential part of transparent boundary conditions for certain hyperbolic systems of second-order equations. (English. Russian original) Zbl 1183.35195 Dokl. Math. 79, No. 3, 412-414 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 5, 602-604 (2009). MSC: 35L53 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Dokl. Math. 79, No. 3, 412--414 (2009; Zbl 1183.35195); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 5, 602--604 (2009) Full Text: DOI
Zaitsev, N. A.; Sofronov, I. L. Use of transparent boundary conditions for solution of two-dimensional elasto-dynamics problems with azimuthal anisotropy. (Russian) Zbl 1137.74323 Mat. Model. 19, No. 8, 49-54 (2007). Reviewer: Sergei Georgievich Zhuravlev (Moskva) MSC: 74B20 35J45 35L40 PDFBibTeX XMLCite \textit{N. A. Zaitsev} and \textit{I. L. Sofronov}, Mat. Model. 19, No. 8, 49--54 (2007; Zbl 1137.74323) Full Text: MNR
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation. (English) Zbl 1066.65081 Kornhuber, Ralf (ed.) et al., Domain decomposition methods in science and engineering. Selected papers of the 15th international conference on domain decomposition, Berlin, Germany, July 21–25, 2003. Berlin: Springer (ISBN 3-540-22523-4/pbk). Lecture Notes in Computational Science and Engineering 40, 141-148 (2005). MSC: 65M06 35Q55 PDFBibTeX XMLCite \textit{A. Arnold} et al., Lect. Notes Comput. Sci. Eng. 40, 141--148 (2005; Zbl 1066.65081) Full Text: DOI
Arnold, A.; Ehrhardt, M.; Sofronov, I. A fast method to implement non-local discrete transparent boundary conditions for the Schrödinger equation. (English) Zbl 1201.65149 PAMM, Proc. Appl. Math. Mech. 2, 424-425 (2003). MSC: 65M06 35Q55 PDFBibTeX XMLCite \textit{A. Arnold} et al., PAMM, Proc. Appl. Math. Mech. 2, 424--425 (2003; Zbl 1201.65149) Full Text: DOI
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. (English) Zbl 1085.65513 Commun. Math. Sci. 1, No. 3, 501-556 (2003). MSC: 65M06 65M12 35Q40 65M15 PDFBibTeX XMLCite \textit{A. Arnold} et al., Commun. Math. Sci. 1, No. 3, 501--556 (2003; Zbl 1085.65513) Full Text: DOI
Coclici, C. A.; Sofronov, I. L.; Wendland, W. L. The far-field modelling of transonic compressible flows. (English) Zbl 0980.35132 Math. Bohem. 126, No. 2, 293-305 (2001). MSC: 35Q35 76H05 35M20 45E05 65M55 PDFBibTeX XMLCite \textit{C. A. Coclici} et al., Math. Bohem. 126, No. 2, 293--305 (2001; Zbl 0980.35132) Full Text: EuDML
Sofronov, Ivan L. An exact artificial boundary condition on a circle for the two-dimensional wave equation. (English) Zbl 1013.65114 Int. J. Numer. Model. 13, No. 5, 385-396 (2000). MSC: 65M70 35L05 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Int. J. Numer. Model. 13, No. 5, 385--396 (2000; Zbl 1013.65114) Full Text: DOI
Ryaben’kii, Victor S.; Sofronov, Ivan L. Difference potentials for the Helmholtz equation in exterior domains. (English) Zbl 0964.65118 Appl. Numer. Math. 33, No. 1-4, 533-540 (2000). MSC: 65N06 35J05 78A45 78M20 PDFBibTeX XMLCite \textit{V. S. Ryaben'kii} and \textit{I. L. Sofronov}, Appl. Numer. Math. 33, No. 1--4, 533--540 (2000; Zbl 0964.65118) Full Text: DOI
Sofronov, Ivan L. Highly-accurate artificial boundary conditions for unsteady transonic flow problems in wind tunnels. (English) Zbl 0929.35117 Fey, Michael (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the 7th international conference, Zürich, Switzerland, February 1998. Vol. II. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 130, 915-924 (1999). Reviewer: S.Nocilla (Torino) MSC: 35Q35 76H05 PDFBibTeX XMLCite \textit{I. L. Sofronov}, ISNM, Int. Ser. Numer. Math. 130, 915--924 (1999; Zbl 0929.35117)
Sofronov, Ivan L. Artificial boundary conditions of absolute transparency for two- and three-dimensional external time-dependent scattering problems. (English) Zbl 0926.35070 Eur. J. Appl. Math. 9, No. 6, 561-588 (1998). Reviewer: S.Jiang (Beijing) MSC: 35L05 65M70 35L15 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Eur. J. Appl. Math. 9, No. 6, 561--588 (1998; Zbl 0926.35070) Full Text: DOI
Sofronov, I. L. The conditions of absolute transparency for wave equation. (Russian. English summary) Zbl 0848.73021 Inst. Prikl. Mat. Im. M. V. Keldysha Ross. Akad. Nauk, Mosk., Prepr. 76, 25 p. (1993). MSC: 74J10 35L05 76Q05 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Inst. Prikl. Mat. Im. M. V. Keldysha Ross. Akad. Nauk, Mosk., Prepr. 76, 25\,p. (1993; Zbl 0848.73021)
Sofronov, I. L. Condition of absolute transparency on sphere for wave equation. (English) Zbl 0870.65087 Morgan, K. (ed.) et al., Finite elements in fluids: new trends and applications. Proceedings of the 8th international conference, Barcelona, Spain, September 20-23, 1993. Part II. Barcelona: Centro Internacional de Métodos Numéricos en Ingenería. 1387-1396 (1993). MSC: 65M70 35L05 PDFBibTeX XMLCite \textit{I. L. Sofronov}, in: Finite elements in fluids: new trends and applications. Proceedings of the 8th international conference, Barcelona, Spain, September 20-23, 1993. Part II. Barcelona: Centro Internacional de Métodos Numéricos en Ingenería; Swansea: Pineridge Press. 1387--1396 (1993; Zbl 0870.65087)
Sofronov, I. L. Conditions for complete transparency on the sphere for the three- dimensional wave equation. (English. Russian original) Zbl 0799.35141 Russ. Acad. Sci., Dokl., Math. 46, No. 2, 397-401 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 6, 953-957 (1992). Reviewer: V.Lovicar (Praha) MSC: 35L15 35L05 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Russ. Acad. Sci., Dokl., Math. 46, No. 2, 397--401 (1992; Zbl 0799.35141); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 6, 953--957 (1992)
Sofronov, I. L. A fastly converging method for solving the Euler equations. (Russian) Zbl 0728.65103 Zh. Vychisl. Mat. Mat. Fiz. 31, No. 4, 575-591 (1991). Reviewer: R.D.Lazarov (Sofia) MSC: 65Z05 65M06 65M12 35Q05 76H05 76B10 76G25 76J20 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Zh. Vychisl. Mat. Mat. Fiz. 31, No. 4, 575--591 (1991; Zbl 0728.65103)
Sofronov, I. L. A rapidly converging method for solving the Euler equation. (English. Russian original) Zbl 0779.65085 Comput. Math. Math. Phys. 31, No. 4, 66-78 (1991); translation from Zh. Vychisl. Mat. Mat. Fiz. 31, No. 4, 575-591 (1991). MSC: 65Z05 65M06 65M12 35Q05 76H05 76B10 76G25 76J20 PDFBibTeX XML Full Text: DOI
Sofronov, I. L. A numerical iterative method for solving regular elliptic problems. (English. Russian original) Zbl 0708.65098 U.S.S.R. Comput. Math. Math. Phys. 29, No. 3, 193-201 (1989); translation from Zh. Vychisl. Mat. Mat. Fiz. 29, No. 6, 923-934 (1989). MSC: 65N22 65F10 35J25 PDFBibTeX XMLCite \textit{I. L. Sofronov}, U.S.S.R. Comput. Math. Math. Phys. 29, No. 3, 193--201 (1989; Zbl 0708.65098); translation from Zh. Vychisl. Mat. Mat. Fiz. 29, No. 6, 923--934 (1989) Full Text: DOI
Sofronov, I. L. A numerical iteration method for solving regular elliptic problems. (Russian) Zbl 0692.65047 Zh. Vychisl. Mat. Mat. Fiz. 29, No. 6, 923-934 (1989). Reviewer: E.D’yakonov MSC: 65N22 65F10 35J25 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Zh. Vychisl. Mat. Mat. Fiz. 29, No. 6, 923--934 (1989; Zbl 0692.65047)
Sofronov, I. L. A new method of numerical solution of regular elliptic problems. (English. Russian original) Zbl 0659.65113 Sov. Math., Dokl. 36, No. 2, 361-365 (1988); translation from Dokl. Akad. Nauk SSSR 269, 1057-1061 (1987). Reviewer: V.L.Makarov MSC: 65N35 35J40 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Sov. Math., Dokl. 36, No. 2, 361--365 (1988; Zbl 0659.65113); translation from Dokl. Akad. Nauk SSSR 269, 1057--1061 (1987)
Ryaben’kij, V. S.; Sofronov, I. L. Numerical solution of spatial external problems for the Helmholtz equation by the method of difference potentials. (Russian) Zbl 0624.35020 Numerical modelling in aerohydrodynamics, Collect. Artic., Moskva 1986, 187-201 (1986). Reviewer: J.Appell MSC: 35J05 35A35 65N06 PDFBibTeX XML
Reznik, A. A.; Ryaben’kij, V. S.; Sofronov, I. L.; Turchaninov, V. I. An algorithm for the method of difference potentials. (English. Russian original) Zbl 0608.65072 U.S.S.R. Comput. Math. Math. Phys. 25, No. 5, 144-151 (1986); translation from Zh. Vychisl. Mat. Mat. Fiz. 25, No. 10, 1496-1505 (1985). MSC: 65N35 65R20 35J05 35C15 PDFBibTeX XMLCite \textit{A. A. Reznik} et al., U.S.S.R. Comput. Math. Math. Phys. 25, No. 5, 144--151 (1986; Zbl 0608.65072); translation from Zh. Vychisl. Mat. Mat. Fiz. 25, No. 10, 1496--1505 (1985) Full Text: DOI
Sofronov, I. L. Nondegeneracy of the equations related to the method of difference potentials. (English) Zbl 0595.65060 Funct. Anal. Appl. 18, 347-349 (1984). MSC: 65J10 65N12 35J05 47A50 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Funct. Anal. Appl. 18, 347--349 (1984; Zbl 0595.65060) Full Text: DOI
Sofronov, I. L. On the non-degeneracy of equations connected with the method of difference potentials. (Russian) Zbl 0576.65045 Funkts. Anal. Prilozh. 18, No. 4, 94-95 (1984). Reviewer: K.Najzar MSC: 65J10 65N12 35J05 47A50 PDFBibTeX XMLCite \textit{I. L. Sofronov}, Funkts. Anal. Prilozh. 18, No. 4, 94--95 (1984; Zbl 0576.65045)