Anatoly Solomonovich Apartsyn. Scientific heritage

S. V. Solodusha

The Bulletin of Irkutsk State University. Series Mathematics, Tome 50 (2024), pp. 170-179

Résumé

A brief overview of the main directions of scientific activity of A. S. Apartsin in the development of the theory of unstable problems of computational mathematics is given.The theoretical and applied results of research by his colleagues and students are presented.

Détail

Keywords: Volterra integral equations of the first kind, numerical methods, inverse and ill-posed problems.

Bibliographie

[1] Apartsyn A.S., “On the theory of multilinear Volterra equations of the first kind”, Optimizatsiya, upravlenie, intellekt, 2005, no. 1(9), 5–27 (in Russian)

[2] Apartsyn A.S., Nonclassical Linear Volterra Equations of the First Kind, VSP, Utrecht-Boston, 2003, 168 pp. | MR | Zbl

[3] Apartsyn A.S., “New Algorithm for Modeling Nonlinear Dynamic Systems Based on Volterra Polynomials”, Optimizatsiya, upravlenie, intellekt, 5 (2000), 26–32 (in Russian)

[4] Apartsyn A.S., “On new classes of linear multidimensional equations of the first kind of Volterra type”, Izvestiya vysshikh uchebnykh zavedeniy. Matematika, 11 (1995), 28–41 (in Russian) | MR | Zbl

[5] Apartsyn A.S., “Multilinear Volterra equations of the first kind”, Automation and Remote Control, 65:2 (2004), 263–269 | DOI | MR | Zbl

[6] Apartsin A.S., “On the application of various quadrature formulas for the approximate solution of Volterra integral equations of the first kind by the method of quadrature sums”, Differentsial'nye i integral'nye uravneniya, 2, Irkutsk State University Publ., Irkutsk, 1973, 107–116 (in Russian)

[7] Apartsin A.S., “On the convergence of numerical methods for solving a Volterra bilinear equations of the first kind”, Computational Mathematics and Mathematical Physics, 47:8 (2007), 1323–1331 | DOI | MR

[8] Apartsyn A.S., “On Volterra integral equations of the first kind in the theory of developing systems”, Chislennye metody optimizatsii i analiza, Nauka Publ., Novosibirsk, 1992, 358–67 (in Russian) | MR | Zbl

[9] Apartsyn A.S., “Polilinear integral Volterra equations of the first kind: the elements of the theory and numeric methods”, The Bulletin of Irkutsk State University. Series Mathematics, 2007, no. 1, 13–41 (in Russian) | MR

[10] Apartsin A.S., “Polynomial Volterra integral equations of the first kind and the Lambert function”, Proceedings of the Steklov Institute of Mathematics, 280, S1 (2013), 26–38 | DOI | MR

[11] Apartsin A.S., Bakushinsky A.B., “Approximate solution of Volterra integral equations of the first kind by the method of quadrature sums”, Differentsial'nye i integral'nye uravneniya, 1, Irkutsk State University Publ., Irkutsk, 1972, 248–258 (in Russian)

[12] Apartsyn A.S., Karaulova I.V., Markova E.V., Trufanov V.V., “Application of Volterra integral equations for modeling strategies of technical upgrading electricity”, Elektrichestvo, 10 (2005), 69–75 (in Russian)

[13] Apartsyn A.S., Markova E.V., Sidler I.V., “Influence of Economic Indices on the Solution to the Optimization Problem of the Age Structure of Power Plants Equipment”, The Bulletin of Irkutsk State University. Series Mathematics, 25 (2018), 19–32 (in Russian) | DOI | MR | Zbl

[14] Apartsyn A.S., Markova E.V., Sidler I.V., “Integral model of developing system without prehistory”, Tambov University Reports. Series: Natural and Technical Sciences, 23:123 (2018), 361–367 (in Russian) | DOI

[15] Apartsyn A.S., Markova E.V., Trufanov V.V., “Analysis of optimal strategies of technical re-equipment of electric energy systems”, Proceedings of XII Baikal International School-Seminar “Optimization Methods and their Applications”, v. 4, ESI SB RAS Publ., Irkutsk, 2001, 25–30 (in Russian)

[16] Apartsyn A.S., Markova E.V., Trufanov V.V., Integral models of electric power systems development, ESI SB RAS Publ., Irkutsk, 2002, 36 pp. (in Russian)

[17] Apartsyn A.S., Markova E.V., Trufanov V.V. On the finding optimal strategies for long-term development of electric power systems based on integral models by V. M. Glushkov, Proceedings of the II International Conf. “Mathematical Modeling Tools”, SPbSTU Publ., St. Petersburg, 1999, 118–123 (in Russian)

[18] Apartsyn A.S., Sidler I.V., “Study of test Volterra equations of the first kind in integral models of developing systems”, Trudy Instituta matematiki i mekhaniki UrO RAN, 24, no. 2, 2018, 24–33 (in Russian) | DOI | MR

[19] Apartsin A.S., Sidler I.V., “On the Test Volterra Equations of the First Kind in the Integral Models of Developing Systems”, Automation and Remote Control, 79:4 (2018), 604–616 | DOI | MR | Zbl

[20] Apartsyn A.S., Sidler I.V., “The test Volterra equation of the first kind in integral models of developing systems containing $n$ age groups”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018), 168–179 (in Russian) | DOI

[21] Apartsyn A.S., Solodusha S.V., Tairov E.A., “Mathematical models of nonlinear dynamics based on Volterra series and their applications”, Izvectiya RAEN. Matematika. Matematicheskoe modelirovanie. Informatika i upravlenie, 1:2 (1997), 115–125 (in Russian) | Zbl

[22] Tairov E.A., Apartsyn A.S., “Construction of integral dynamic models of heat exchangers and their study on a high-temperature circuit”, Izvectiya RAN. Energetika, 1996, no. 3, 85–98 (in Russian)

[23] Apartsyn A. S., “Mathematical modeling the dynamic systems and objects with the help of the Volterra integral series”, EPRI-SEI Joint seminar of methods for solving the problems on energy power systems development and control (Beijing, China, 1991), 117–132

[24] Apartsyn A. S., “Some ill-posed problems and their applications in energy research”, Sov. Tech. Rev. A. Energy, 6, no. 1, Harwood Academic Publishers GmbH, USA, 1992, 65–125

[25] Apartsin A. S., Solodusha S. V., “Mathematical Simulation of Nonlinear Dynamic Systems by Volterra Series”, Engineering Simulation, 17 (2000), 143–153