Valentin Georgiev

@uni-plovdiv.bg

Faculty of Mathematics and Informatics
University of Plovdiv "Paisii Hilendarski"

Valentin Georgiev


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https://researchid.co/valentin_georgiev

EDUCATION

University of Plovdiv "Paisii Hilendarski" - Applied Mathematics - bachelor's degree

RESEARCH, TEACHING, or OTHER INTERESTS

Analysis, Numerical Analysis
8

Scopus Publications

Scopus Publications

  • ON THE CONNECTION BETWEEN FIXED POINT THEOREMS ON METRIC SPACES WITH GRAPHS AND P SETS
    Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov
    Annual of Sofia University St Kliment Ohridski Faculty of Mathematics and Informatics, 2025
    The Banach contraction principle is one of the most famous and applied results in recent mathematical history. Due to its utility, plenty of generalizations have been established. One of them considers a contraction principle on metric spaces with graphs, while another confines the contraction principle to pairs of elements inside a $\mathbb{P}$ set, a generalization of partial orders. In this work we examine the similarities of both approaches, establishing the connection between theorems of metric spaces with graphs and metric spaces with $\mathbb{P}$ sets and restating results from one approach to the other and vice versa.
  • An Analysis of a Family of Difference Schemes for Solving Hyperbolic Partial Differential Equations †
    Pavlina Atanasova, Stoyan Cheresharov, Valentin Georgiev
    Mathematics, 2025
    Partial differential equations are an integral part of modern scientific development. Hyperbolic partial differential equations are encountered in many fields and have many applications—both linear and nonlinear types, with some being semilinear and quasilinear. In this paper, a family of implicit numerical schemes for solving hyperbolic partial differential equations is derived, utilizing finite differences and tridiagonal sweep. Through the discrete Fourier transform, a necessary and sufficient condition for convergence is proven for the linear version of the family of difference schemes, expanding the known results on boundary conditions that ensure convergence. Numerical verification confirms the found condition. A series of experiments on different boundary conditions and semilinear hyperbolic PDEs show that the same condition seems to also hold in those cases. In view of the results, an optimal subset of the family is found. A comparison between the implicit schemes and an explicit analogue is conducted, demonstrating the gained efficiency of the implicit schemes.
  • Further Results on the Mathematical Theory of Motion of Researchers Between Research Organizations
    Pavlina Atanasova, Valentin Georgiev, Magdalena Veselinova, Nikolay Vitanov
    Mathematics, 2025
    Recently, Vitanov and Dimitrova presented a mathematical theory of motion of researchers between research organizations. They obtained analytical results based on exact solutions for a specific case of a model system of ordinary differential equations for studying a system of research organizations. In this article, we investigate the system of model equations of Vitanov and Dimitrova analytically and numerically, obtaining several new results. We provide sufficient conditions for the concavity of the solutions of the system and make a comparison with an exact solution. We numerically examine the effect of several parameters on the concavity. We further inspect the influence of the parameters on whether the solution has overall increased or decreased compared with the initial condition.
  • Numerical Analysis of a Difference Scheme Family for Solving Semilinear Hyperbolic PDEs
    Pavlina Atanasova, Valentin Georgiev
    Springer Proceedings in Mathematics and Statistics, 2025
  • On the Special Cases of the Jacobi Elliptic Function Solutions of the (2+1)-Dimensional Sine-Gordon Equation
    Pavlina Atanasova, Valentin Georgiev
    Springer Proceedings in Mathematics and Statistics, 2025
  • A Generalization of Fixed-Point Theorems for Mappings with a Contractive Iterate
    Valentin Georgiev, Boyan Zlatanov
    Mathematics, 2024
    In this paper, a generalization of fixed-point mappings with an iterate at a point in complete metric spaces is shown, using the notions of T-closed sets and i-P-regularity/d-P-regularity, proving conditions for the existence and uniqueness of the fixed point. Examples are provided to illustrate the results and an application to coupled fixed points is shown.
  • A variational principle, fixed points and coupled fixed points on P sets
    Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov
    Journal of Fixed Point Theory and Applications, 2024
  • REGIONS OF EXISTENCE OF ANALYTICAL SOLUTIONS OF THE (2+1)-DIMENSIONAL SINE-GORDON EQUATION
    Journal of Theoretical and Applied Mechanics Bulgaria, 2024

Publications

V. Georgiev, P. Atanasova, On the Analytic Solutions of the Sine-Gordon Equation, Scientific researches of the Union of Scientists in
Bulgaria-Plovdiv. Series C. Techincs and Echnologies, Vol. 21, ISSN: 1311-9192 (print), 2534-9376 (online), 2024

Atanasova, P., Georgiev, V. (2023). Numerical Solving of the Sine-Gordon of the International Scientific Conference “Informatics, Mathematics, Education and Their Applications” IMEA’2023, 23-30, 29 Nov - 1 Dec 2023, Pamporovo, Bulgaria, ISBN: 978-619-7663-79-2
Link:

Georgiev, V. and Yotov, K. (2024) “Analysis of Suicide Risk in European Countries Using Artificial Intelligence Methods”, Computer Science and Interdisciplinary Research Journal, 1(1), p. 7. Available at: (Accessed: 20 August 2024).

Hadzhikolev, E., Hadzhikoleva, S. and Georgiev, V. (2024) “Impact of Global Country Indicators on Life Expectancy”, Computer Science and Interdisciplinary Research Journal, 1(1). Available at: (Accessed: 1 September 2024).

Valentin Georgiev, Vasil Zhelinski, Boyan Zlatanov, Best Proximity Point Theorem for Mappings with a Contractive Iterate on P Sets, MATTEX 2024, CONFERENCE PROCEEDING, v. 1, (2024) 79-90, ISSN: 1314-3921