Education

1957 - 1963 -  Penza Industrial Institute (Penza) (the latter, in 1961, it was renamed as the Penza Polytechnic Institute. (Electrical Engineering Diploma).  

1964 – 1968  -  Department of  Mechanics and Mathematics (Kazan State University, (Diploma with honors in Mathematics).

1968 -1971 postgraduate student at Department of Mathematical Analysis of Kazan  State University.

1972  -  received Ph.D. in "Mathematical Analysis" (Kazan State University). The thesis title is  “Approximate solution of singular integral equations”.

1991 -  received Doctor of Science in "Computational Mathematics" (Computing Center of the Siberian Branch of the USSR  Academy of Sciences). The thesis title is "Optimal in accuracy algorithms for calculating singular integrals and solving singular integral equations."

Professional Experience

I am currently working as Professor, Department "Higher Mathematics",  Penza State University. 

Grants:

3 grants from the Russian Foundation for Basic Research,

3 grants from the Ministry of Higher Education of the Russian Federation,

 grant from the Russian Scientific Humanitarian Foundation,

4 research topics carried out on the tasks of the Federal Agency for Education of the Russian Federation,  

two grants from the International Science Foundation. Twice was awarded the State Scientific Scholarship for outstanding scientists of the Russian Federation. 

Member of the editorial boards of the journals “University proceedings, Volga region, Physical and mathematical sciences, Mathematics,”, and “Journal of the Middle Volga Mathematical Society”. Member of the American Mathematical Society, European Mathematical Society, Member of the Research Council of the American Biographical Institute.

Soros Professor, Honorary worker of higher professional education of the Russian Federation,  Honored worker of professional education of the Penza region.         

 Monographs

 1.     1Boykov I.V.  Optimal with Respect to Accuracy Algorithms for Approximate Calculation   of  Singular Integrals.-     Publishing House of the Saratov State University, Saratov, 1983, 210 p.

2.     Boykov I.V. Passive and adaptive approximation algorithms for calculation   of  singular integrals. - Part 1.Publishing house of Penza State Technical University. Penza. 995. 214 p.

3.     Boykov I.V. Passive and adaptive approximation algorithms for calculation   of singular integrals. - Part 2 .Publishing house of Penza State Technical University Penza.1995.128 p.

4.     Boykov I.V. Dobrynina N.F. Domnin L.N. Approximate Methods for Calculation of Hadamard integrals and solution of hypersingular integral equations.- Publishing house of Penza State Technical University. Penza 1996. 188 p.

5.     Boykov I.V. Approximate solution of singular integral equations. Publishing house of Penza State University. 2004. 316 p.

6.     Boykov I.V. Approximate methods for calculating singular and hypersingular integrals. Part one. Singular integrals. Penza:Publishing house of Penza State University. 2005.360 p.

7.     Boykov I.V. Optimal Methods for Function Approximation and Calculation of Integrals. - Penza: Publishing house of Penza State University. 2007. 236 p.

8.     Boykov I.V. Stability of solutions of differential equations. - Penza: Publishing house of Penza State University. 2008. 244 p.

9.     Boykov I.V. Approximate methods for calculating singular and hypersingular integrals. Part two. Hypersingular integrals. Penza:Publishing house of Penza State University. 2009. 252 p.

10.  Boykov I.V., Boykova A.I. Approximate methods for solving direct and inverse problems of gravity exploration. Penza: Publishing House of the Penza State University. 2013. 510 p.

11.  Boykov I.V., Krivulin N.P. Analytical and numerical methods for identification of dynamical systems. - Penza: Publishing House of the Penza State University. 2016. 398 p.

12.  Boykov I.V. Approximate Methods for Solving Hypersingular Integral Equations. In the book "Topics in Integral and   Integro-Difference Equations. Theory fnd Applications. Editors Harenfra Singh, Hemen Dutta, Marcelo M. Cavalcanti. 2021. PP. 63-102.

Patents, copyright certificates

1.     Boykov I.V., Dobrovinsky I.R., Dzyubenko V.M., Ivanov V.A., Vorozheikin I.I. A device for measuring the position of the axis of the welding joint. Copyright certificate N899294

2.     Boykov I.V., Dobrovinsky I.R., Ivanov V.A., Vorozheikin I.I. Device for measuring the excess of the edges of the welded joint Author's certificate N916171

3.     Boykov I.V., Dobrovinsky I.R., Dzyubenko V.M., Ivanov V.A. Device for measuring the width of the welded joint. Copyright certificate N899293

4.     Boykov I.V., Knyazkov V.S., Volchenskaya T.V., Afonin S.A. Cell of homogeneous computing environment. Copyright certificate.N1513471

5.     Boykov I.V. Device for correcting output signals. Patent 1705768. 1989

6.     Boykov I.V. Transient response device.- Patent N 2069370. 1996

7.     Boykov I.V., Strukov V.I., Semerich Yu.S., Vyazovskaya Yu.Yu. The program for determining the degree of patient damage by osteoporosis. Certificate of state registration of the computer program. No. 2013660284. Registration date 10.30. 2013.

8.     Boykov I.V., Grinchenkov G.I. Approximation of classes of functions with power singularities on the boundary of the domain (class $Q_{r,gamma}$. Certificate of state registration of the computer program. No. 2014615847. Date of registration 04.06. 2014.

9.     Boykov I.V., Ryazantsev V.A. Adaptive difference algorithm for solving parabolic equations on grids with variable structure. State registration certificate for a computer program. No. 2014663162. Date of registration 05.11. 2014.

10.  Boykov I.V., Ryazantsev V.A. Adaptive difference algorithm for potential fields recovery. Certificate of state registration of the computer program. No. 2015610120. Date of registration 19.05. 2015.

11.  Boykov I.V., Syomov M.A. Software package for calculating hypersingular integrals. Certificate of state registration of the computer program. No. 2015619801. Date of registration 15.09. 2015.

12.  Boykov I.V., Kalashnikov D.M. Means of neural network biometric recognition by voice at a noise level higher than the signal level. Certificate No. 2016663957 on state registration of the computer program.

 13.  Aikashev P.V., Boykov I.V. Software package for the approximate solution of the integral equation of the first kind on fractals and the synthesis of fractal antennas. Certificate No. 2018612927 on state registration of the computer program dated  01.03.2018

14.  Pivkina A.A., Boykov I.V.  Software package for approximate solution of system of Ambartsumyan's singular integral equations by the spline-collocation method with splines of zero and first degrees. Certificate No. 2022663909 on state registration of the computer program dated   21.07.2022.

15.  Pivkina A.A., Boykov I.V. Software package for approximate reconstruct of one-dimensional signal from the amplitude of its spectrum. Certificate No. 2022681401 on state registration of the computer program dated 14.11.1022.

16.   Aikashev P.V., Boykov I.V. Software package for approximate solution of the Pocklington equation. Certificate No. 2022662731 on state registration of the computer program dated 07.07.22

17.  Pivkina A.A., Boykov I.V. Software package for approximate solution of Ambartsumyan's singular integral equation by the spline-collocation method with splines of zero and first degrees. Certificate No. 2022616628 on state registration of the computer program  15.04.2022.

 Selected  Publications     

 1.     Boykov I. V. On the approximate solution of singular     integral equations//Reports of the Academy of Sciences of the USSR  1972. Volume 203, No. 3. P. 511-514.

2.     Boikov  I. V. The approximate solution of singular integral equations Mathematical notes of the Academy of Sciences of the USSR volume 12, pages 541–546 (1972)

3.     Boykov I.V. On one direct method for solving singular integrals Equations// U.S.S.R. Comput. Math. Math. Phys., 12:6 (1972), 13–25

4.     I.V. Boikov, Y.I. Zhechev, “On the approximate solution of singular integro-differential equations. I (Linear equations)”//Differ. Equations, 9:8 (1973), 1493–1502

5.     I. V. Boikov, On the approximate finding of all solutions of functional equations, Dokl. AN

USSR, 1974, volume 217, number 6, 1241–1244

6.     I. V. Boikov, On optimal algorithms for multiple singular integrals// Dokl.  Academy of Sciences of the USSR, 1974, volume 219, number 1, 15–18

7.     I. V. Boikov, Approximate solution of singular integral equations, Dokl. USSR Academy of Sciences, 1975, vol 224, number 6, 1241–1244

8.     I.V. Boikov, Y.I. Zhechev, “On the approximate solution of singular integro-differential equations. II. Nonlinear Equations”// Differential Equations, 11:3 (1975), 562–571

9.     Boykov I.V. Optimal cubature formulas for calculating multidimensional integrals on the class //U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 110–117

10.  Boykov I.V. On one adaptive algorithm for approximating functions // Comput. Math. Math. Phys., 33:11 (1993), 1437–1446

11.  Boykov I.V. Approximation of some classes of functions local splines// Computational Mathematics and Mathematical Physics, 1998, 38:1, 21–29

12.  Boikov I.V. On the stability of solutions of differential and difference equations in critical cases// Soviet Math. Dokl. Vol. 42 (1991), No 2. P.630-632.

13.  I. V. Boikov, On the stability of solutions of differential and difference equations with non-differentiable right-hand sides.// Different. Equ. 29:8 (1993), 1259–1261

14.  I. V. Boikov. Adaptive algorithms for computing singular integrals.//Different. Equ. 29:9 (1993), 1376–1382

15.  Boikov I.V.  An approximation of analitical functions by local splines// Theory of Approximation and its Applications. 1996. V.12, N3. Sept. P.59-67.

16.  I. V. Boikov, Optimal methods for solving some classes of integral equations.// Differ. Equ., 33:9 (1997), 1159–1170

17.   Boykov I.V. On the stability of solutions of differential equations with aftereffect. //  

Differ. Equ., 34:8 (1998), 1138–1141

18.  Boykov I.V. Complexity-optimal approximation algorithms solutions of integral equations //Differ. Equ., 34:9 (1998), 1242–1247

19.  Boykov I.V. , Kudryashova N.Yu. Approximate methods for singular integral equations in exceptional cases Differential Equations. 2000, 36(9):1360-1369.

DOI: 10.1007/BF02754309

20.  Boikov I.V., Numerical methods of computation of singular and hypersingular integrals, International Journal of Mathematics and Mathematical Sciences,  28(3), (2001), 127-179.

DOI: 10.1155/S0161171201010924

21.  Boikov  I. V. & A. N. Tynda Accuracy-Optimal Approximate Methods for Solving Volterra Integral Equations// Differential Equations volume 38, pages1305–1312 (2002)

22.  Boikov I.V., Boikova A.I. Stability of solution of differential equations. Preprints of the NATO Advanced Study Institute on Virtual nonlinear multibody systems, V 1, Prague, 2002, p.33-39

23.  Boikov I.V. STABILITY OF HOPFIELD NEURAL NETWORKS.//  Automation and Remote Control. 2003. Т. 64. № 9. С. 1474-1487.

24.  Ilya V. Boikov  and Alexander G. Ramm. Optimal with Respect to Accuracy Algorithms for Calculation of Multidimensional Weakly Singular Integrals and Applications to Calculation of Capacitances of Conductors of Arbitrary Shapes//Acta Applicandae Mathematicae (2003) V. 79, N 3. P.281-326.

   25.  I.V. Boikov   A. N. Tynda  Approximate Solution of Nonlinear Integral Equations of the       Theory of Developing Systems// Differential Equations volume 39, pages1277–1288 (2003)

25.   Boykov  I. V., A.I. Boykova, E.S. Ventsel Fundamental Solutions for Thick Sandwich Plate// Engineering Analisis and Boundary Elements. 2004. V. 28. P. 1437 - 1444.

26.  Boikov  I. V. Superconvergence of solutions of multidimensional Fredholm integral equations// Differential Equations volume 40, pages1757–1763 (2004)

27.  Boikov I.V. The Brockett stabilization problem// Automation and Remote. 2005. V. 66, N 5, pp 745-751.

28.  Boykov I. V.  On a stability criterious for solutions of systems of nonlinear differential equations// Differential equations. 2006 V. 42, N. 1. P. 1-9.

29.  Boykov I.V., Boykova A. I., Ventsel E. S. An approximation methods for evaluating hypersingular integrals// Engineering analysis with Boundary elements. 2006.V. 30. pp. 799-807.

30.  Boikov, I.V. On a stability criterion for solutions of systems of nonlinear differential equations. Diff Equat 42, 1–9 (2006). https://doi.org/10.1134/S0012266106010010

31.  Boikov I.V.  On lower Bounds on the Complexity of Solution of Integral Equations// Differensial equations. 2008. V. 44. N 8. P. 1131-1134.

32.  Boykov I. V., E.S. Ventsel, A.I Boykova Accuracy optimal methods for evaluating hypersingular integrals// Applied Numerical, 2009, V. 59, N. 6, pp. 1366-1385.

33.  Boikov I.V. , Kravchenko M. V., Kryuchko V.I.  The approximate method for reconstruction the potential fields// Izvestia Physics of the Solid Earth.  2010. V. 46, N 4. P. 339-349.

34.  Boykov I. V., E.S. Ventsel, A.I Boykova  An approximate solution of hypersingular integral equations// Applied Numerical Mathematics 60 . v. 6, (2010) P. 607-628.

 35.  Boikov I.V., Boikova A.I. Iterative Methods for a Class of Convolution Equations// Differential Equations. 2010. V. 46, N 9. P.1313- 1319.

36.  Boikov I. V. On a continuous method for solving nonlinear operator equations// Differential equations. 2012, V. 48, No 9. P. 1308 - 1314.

37.  Boikov I.V., Krivulin N.P.  Recovery of the parametres of linear systems described by differential equations with variable coefficients//Measurement Techniques. July 01, 2013, V. 56, P. 359-367.

38.  Boykov I.V., Ventsel E.S.,  Roudnev V.A., Boykova A.I.

39.  An approximate solution of nonlinear hypersingular integral equations//Applied Numerical Mathematics. Volume 86, December 2014, Pages 1-21.

40.  Boykov I.V., Tynda A.N.  Numerical methods of optimal accuracy for weakly singular Volterra integral equations// Annals of functional Analysis. 2015. V. 6, No 4. P. 114 -133.

41.  Boikov I.V., M.A. Syomov. On a method of calculation of hypersingular integrals// Russian Mathematics. March 2016, Volume 60, Issue 3, pp 1-13.

42.  Boikov I.V. Optimal cubature formulas for calculation of multidimensional integrals in weighted Sobolev spaces//Siberian Mathematical Journal, 2016 Vol. 57, No.3, pp.425- 441.

43.  Boikov I.V., Krivulin N.P. Recovering the Input Signals of Discrite Dynamical Systems// Measurement Techniques, 2017, 60(11), 1073-1080.

44.  Boikov I.V. Stability of Steady-State Solutions of Systems of Nonlinear Nonautonomous Delay Differential equations// Differential equations, 2018, V. 54, No 4. P. 1-23.

45.  Boykov I.V.,  Roudnev V.A., Boykova A.I., Baulina O.A.

New iterative method for solving linear and nonlinear hypersingular integral equations//Applied Numerical Mathematics. Volume 127, May 2018, Pages 280-305.

46.  Boikov I.V., Krivulin N.P. Identification of Parameters of Nonlinear Dynamical Systems

Simulated by the Volterra Polynomials//Journal of Applied and Industrial Mathematics, 2018, Vol. 12, No. 2, pp. 1-16.

47.  Boikov I.V., Boikova A.I., Baulina O.A. (2019) Continuous Method for Solution of Gravity Prospecting Problems. In: Nurgaliev D., Khairullina N. (eds) Practical and Theoretical Aspects of Geological Interpretation of Gravitational, Magnetic and Electric Fields. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. P. 55-68.

48.  Boikov  I. V. , N. P. Krivulin  S. V. Abramov V. P. Malanin V. V. Kikit  Recovery of the Input Signals of Eddy-Current Displacement Transducers Under Thermal-Shock Actions// Measurement Techniques. February 2019, Volume 61, Issue 11, pp 1118-1125

49.  Boykov I.V., P.V. Aikashev To the numerical method for synthesis of fractal antennas//2019 International Seminar on Electron Devices Desing and Production (SED).   Prague, Czech Republic. 2019.

50.   Ilya Boykov, Pavel Aikashev To the numerical method for synthesis of fractal antennas//2019 International Seminar on Electron Devices Design and Production (SED 2019). Prague, Czech Republic 23-24 April 2019. IEEE Catalog Number: ISBN: CFP19P59-POD 978-1-5386-5851-2 P. 119 -125.

51.   I. Boikov and P. Aikashev, "Application of Singular Integral Equations to the Study of Automatic Control Problems," 2019 XXI International Conference Complex Systems: Control and Modeling Problems (CSCMP), Samara, Russia, 2019, pp. 261-266.

DOI: 10.1109/CSCMP45713.2019.8976545

52.   I. Boikov and N. Krivulin, "Hardware and Software Methods for Restoring Input Signals of Dynamic Systems with Distributed Parameters. Reduction to the Perfect Device," 2019 XXI International Conference Complex Systems: Control and Modeling Problems (CSCMP), Samara, Russia, 2019, pp. 658-663. DOI: 10.1109/CSCMP45713.2019.8976847

53.   I. V. Boikov and N. P. Krivulin GENERAL PROBLEMS OF METROLOGY AND MEASUREMENT TECHNIQUERECOVERY OF CHARACTERISTICS NON-STATIONARY DYNAMIC SYSTEMS FROM THREE TEST SIGNALS. Measurement Techniques, 63(3), 2020, 158-165 DOI 10.1007/s11018-020-01766-4

54.  Boikov I., Zelina Y., Vasyunin D. Approximate Methods for Solving of Onedimensional Amplitude-phase Problem//Published in: 2020 Moscow Workshop on Electronic and Networking Technologies (MWENT). Date Added to IEEE Xplore: 16 April 2020. Publisher: IEEE. Conference Location: Moscow, Russia, Russia.

DOI: 10.1109/MWENT47943.2020.9067415

55.   I. V. Boikov and V. A. Ryazantsev On Simultaneous Restoration of Density and Surface Equation in an Inverse Gravimetry Problem for a Contact Surface //ISSN 1995-4239, Numerical Analysis and Applications, 2020, Vol. 13, No. 3, pp. 241?257.

DOI: 10.1134/S1995423920030040

56.  Boykov I. V. Ryazantsev V. A. On an iterative method for solution of direct problem for nonlinear hyperbolic differential equations // Journal of the Middle Volga Mathematical Society. 2020. V. 22, Issue 2,  155--163. DOI 10.15507/2079-6900.22.202002.155-163.

57.   Ilya Boykov, Vladimir Roudnev, Alla Boykova.  Methods for Solving Linear andNonlinear Hypersingular Integral Equations //Axioms, 2020, 9(3), 74; https://doi.org/10.3390/axioms9030074 - 01 Jul 2020

58.  Boikov, I.V., Ryazantsev, V.A. On Optimal Approximation of Geophysical Fields. Numer. Analys. Appl. 14, 13–29 (2021). https://doi.org/10.1134/S199542392101002X

59.   I. V. Boykov and V.A.Ryazantsev An Approximate Method for Solvingan Inverse Coefficient Problem for the Heat Equation//ISSN 1990-4789, Journal of Applied and Industrial Mathematics, 2021, Vol. 15, No. 2, pp. 175–189.

Pleiades Publishing, Ltd., 2021.Russian Text The Author(s), 2021, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2021, Vol. 24, No. 2, pp. 5–22.

DOI 10.1134/S1990478921020010

60.  Boykov I.V. Approximate Methods for Solving Hypersingular integral Equations. In the book "Topics in Integral and Integro-Difference Equations. Theory and Applications. Editors Harenfra Singh, Hemen Dutta, Marcelo M. Cavalcanti. PP. 63-102.

61.   I. V. Boykov and N. P. Krivulin Methods for Control of Dynamical Systems with Delayed Feedback – JOURNAL OF MATHEMATICAL SCIENCES Volume 255, Number 5 June 21, 2021, .561--573

https://doi.org/10.1007/s10958-021-05393-4

62.   I. V. Boikov, Ya. V. Zelina Approximate Methods of Solving Amplitude-Phase Problems for Continuous Signals Measurement Techniques. Oct 2021.  64, pages 386–397 (2021)

DOI: 10.1007/s11018-021-01944-y

63.   I. V. Boykov, V. A. Roudnev, A. I. Boykova, N. S. Stepanov. Continuous operator method application for direct and inverse scattering // Journal of the Middle Volga Mathematical Society. 2021. V. 23, № 3.  247 -- 272.

64.  Boykov I. V., Ryazantsev V. A. On the problem of recovering boundary conditions in the third boundary value problem for parabolic equation // University Proceedings. Volga Region. Physical and Mathematical Sciences. 2021. № 2,  3–13. doi:10.21685/2072-3040-2021-2-1

65.   I. V. Boikov, Ya. V. Zelina and D. I .Vasyunin. Approximate methods for solving amplitude-phase problem for discrete signals// Journal of Physics: Conference Series 2099 (2021) 012002 IOP Publishing doi:10.1088/1742-6596/2099/1/012002

66.  Boykov, I.; Roudnev, V.;Boykova, A. Approximate Methods for Calculating Singular and

Hypersingular Integrals with Rapidly Oscillating Kernels. Axioms 2022, 11,150.

https://doi.org/10.3390/axioms11040150

67.  Boykov, I.; Roudnev, V.;Boykova, A.  Stability of Solutions to Systems of Nonlinear Differential Equations with Discontinuous Right-Hand Sides: Applications to Hopfield Artificial Neural Networks. Mathematics 2022, 10, 1524. https:// doi.org/10.3390/math10091524

68.  Boykov, I.V., Boykova, A.I., Potapov, A.A., Rassadin, A.E. (2022). Approximate Methods for Solving Hypersingular Integral Equations on Fractals. In: Skiadas, C.H., Dimotikalis, Y. (eds) 14th Chaotic Modeling and Simulation International Conference. CHAOS 2021. Springer Proceedings in Complexity. Springer, Cham. $https://doi.org/10.1007/978-3-030-96964-6_7$

69.  Boykov I.V., Krivulin N.P. An approximate method for recovering input signals of measurement transducers Measurement Techniques. 2022.

70.  Boykov I.V., Ryazantsev V.A., Potapov A.A., Rassadin A.E. Approximate solution of inverse problems of gravity exploration on fractals// В сборнике: Springer Proceedings in Complexity. 14th. Сер. "14th Chaotic Modeling and Simulation International Conference" 2022. P. 97-108.

71.   I. V. Boikov and A. I. Boikova On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals//Numerical Analysis and Applications, 2022. 2022,V. 15, No. 3,  203–218.  Pleiades Publishing, Ltd., 2022.

72.  Boykov, I.; Roudnev,V.; Boykova, A. Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks. Mathematics 2022, 1, 0. https://https://doi.org/10.3390/math10132207

73.  I.V. Boykov,  P. V. Aykashev, Approximate Methods for Calculating Hypersingular Integrals // ISSN 1063-7842, Technical Physics, 2022. © Pleiades Publishing, Ltd., 2022.

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Povolzhskii Region, Fiziko-Matematicheskie Nauki, 2021, Vol. 57, No. 1, pp. 66–84. DOI: 10.1134/S1063784222070039

74.   I. V. Boykov, and A. A. Shaldaeva Iterative Methods of Solving Ambartsumian Equations.Part 1 // ISSN 1063-7842, Technical Physics, 2022. © Pleiades Publishing, Ltd., 2022. Russian Text © The Author(s), 2022, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Povolzhskii Region, Fiziko-Matematicheskie Nauki, 2022, Vol. 58, No. 2, pp. 14–34. DOI: 10.1134/S1063784222070015

75.  Boykov, I.V., Pivkina, A.A. Iterative Methods of Solving Ambartsumian Equations. Part 2. Tech. Phys. (2022). https://doi.org/10.1134/S1063784222070027

76.  Boykov, I.; Roudnev, V.; Boykova, A. Hypersingular Integral Equations of Prandtl’s Type: Theory, Numerical Methods, and Applications. Axioms 2022, 11, 705. https://doi.org/10.3390/axioms11120705

ORCID: 0000-0002-6980-933X