The Department of Mathematical Modeling was established in 2005.

The head of the department from the beginning its existences is  prof. Piotr Matus (http://im.bas-net.by/~matus/cv.html)

The Department conducts both research and teaching activities.

Our research focuses on mathematical modeling. Mathematical modeling consists of creating a mathematical model representing the initial object and further analysis of the model created by utilizing computational and numerical methods. The results are obtained by following the steps: modeling - creating algorithm – coding, discussion of the numerical results. For every researcher modeling constitutes a universal tool applicable in variety of fields like mathematics, physics, medicine, biotechnology and others.


Employees:

Piotr Matus, Prof. Hab.PhD

Fields of interest: numerical methods for partial differential equations

Current research:

    1. Lemeshevsky Sergey; Matus Piotr; Poliakov Dmitriy, Exact finite-difference schemes, De Gruyter, Berlin, 2016. (monography)

    2. Piotr Matus, Dmitriy Poliakov, Le Minh Hieu On the consistent two-side estimates for the solutions of quasilinear convection-diffusion equations and their approximations on non-uniform grids // Journal of Computational and Applied Mathematics, 2018, Vol. 340, pp. 571-581. https://doi.org/10.1016/j.cam.2017.09.020

    3. P. P. Matus,. M. Hieu , and D. Pylak Monotone Finite-Difference Schemes of Second-Order Accuracy for Quasilinear Parabolic Equations with Mixed Derivatives, Differential Equations, 2019, Vol. 56, No. 3, pp. 1–13.

International cooperation:

    • Creator and managing editor of Computational Methods in Applied Mathematics (5-year IMPACT FACTOR: 1.411)

    • Conducts research in cooperation with scientists from Germany, Russia, Spain, Bulgaria and others

    • Member of Belarusian Mathematical Society

e-mail: matus [at] kul.pl

Aliaksandr Chychuryn, Hab. PhD, Professor of KUL

Fields of interest: differential equations, computer algebra systems

Current research:

    • Chichurin, E. Ovsiyuk, V. Red’kov Modeling the quantum tunneling effect for a particle with intrinsic structure in presence of external magnetic field in the Lobachevsky // Computers and Mathematics with Applications. 2018, 75: P.1550–1565 doi.org/10.1016/j.camwa.2017.11.019

    • Chichurin, H. Shvychkina Computer simulation of two chemostat models for one nutrient resource// Mathematical Biosciences, 278, 2016, p. 30-36. dx.doi.org/10.1016/j.mbs.2016.05.004

    • Alexander Chichurin Computer algorithm for solving of the Chazy equation of the third order with six singular points // Miskolc Mathematical Notes. 2017, Vol. 18: P. 701-715 DOI: 10.18514/ MMN.2017.2232

International cooperation

Participation in projects: Erasmus Mundus, Erasmus+

e-mail: achichurin [at] kul.pl

Małgorzata Nowak-Kępczyk, PhD

Fields of interest: binary, ternary, quaternary structures in mathematics and physics

Current research:

    • Osamu Suzuki, Julian ŠŁawrynowicz, Małgorzata Nowak-Kępczyk, Binary and ternary structures in physics III. Galois-type theory for binary and ternary structures, Bull. Soc. Sci. Lettres Łódź Sér. Rech. Déform. 68 no. 1, (2018) 95 115.

    • Ławrynowicz, J., Suzuki, O., Niemczynowicz, A., & Nowak-Kępczyk, M., Fractals and chaos related to Ising-Onsager-Zhang lattices. Quaternary approach vs. ternary approach, Adv. Appl. Cli. Alg., 29 no.3, 2945 (2019) (2019-04-30) DOI: 10.1007/s00006-019-0957-0

    • Julian Ławrynowicz, Małgorzata Nowak-Kępczyk, and Mariusz Zubert, MATHEMATICS BEHIND TWO RELATED NOBEL PRIZES 2016: IN PHYSICS - TOPOLOGY GOVERNING PHYSICS OF PHASE TRANSITIONS, IN CHEMISTRY – GEOMETRY OF MOLECULAR NANOENGINES, Bulletin des Lettres des Sciences de Łódź, Ser. Rech. Deform. Vol. LXIX no. 1. (2020)

International cooperation

prof. Zhang Zhidong, Institute of Metal Research of Chinese Academy of Sciences, Shenyang, China

prof. Osamu Suzuki, Department of Information Sciences, College of Humanities and Sciences, Nihon University

Sakurajosui 3-25-40, Setagaya-ku, 156-8550 Tokyo, Japan

e-mail: malnow [at] kul.lublin.pl

Dorota Pylak, PhD

Fields of interest: numerical methods, algorithms, programming

Current research:

    • P. P. Matus,. M. Hieu , and D. Pylak Monotone Finite-Difference Schemes of Second-Order Accuracy for Quasilinear Parabolic Equations with Mixed Derivatives, Differential Equations, 2019, Vol. 56, No. 3, pp. 1–13.

    • Dorota Pylak, Paweł Karczmarek and Paweł Wójcik, Approximate Solution of a Singular Integral Equation with a Cauchy Kernel on the Euclidean Plane, Computational Methods in Applied Mathematics, 2017, pp.1-12

    • Piotr Matus, Dmitriy Poliakov, Dorota Pylak, On convergence of difference schemes for Dirichlet IBVP for two-dimensional quasilinear parabolic equations,
      International Journal of Environment and Pollution, Vol. 66, Nos. 1/2/3, 2019

International cooperation

e-mail: dorotab [at] kul.pl

Przemysław Rutka, PhD

Fields of interest: approximation, orthogonal polynomials, algorithms, computer graphics, programming

Current research:

    • P. Rutka, R. Smarzewski, The Szegő-Markov-Bernstein inequalities and barycentric representations of the osculatory interpolating operators for classical iterated weights, Journal of Mathematical Inequalities 13 (2019), 983-999.

    • P. Rutka, R. Smarzewski, Difference inequalities and barycentric identities for classical discrete iterated weights, Mathematics of Computation 88 (2019), 1791-1804.

    • P. Rutka, R. Smarzewski, Explicit barycentric formulae for osculatory interpolation at roots of classical orthogonal polynomials, Mathematics of Computation 86 (2017), 2409-2427.

International cooperation

e-mail: rootus [at] kul.pl

Krystyna Kiersztyn, MSc

Fields of interest: Artificial intelligence, data mining

Current research: Kiersztyn, A., Karczmarek, P., Zhadkovska, K., & Pedrycz, W. "Determination of a Matrix of the Dependencies Between Features Based on the Expert Knowledge." International Conference on Artificial Intelligence and Soft Computing. Springer, Cham, 2018.

International cooperation

e-mail: krystyna.kiersztyn [at] kul.pl

Henryk Malinowski, PhD

Fields of interest: algorithms, programming

Current research:

International cooperation

e-mail: hmalin [at] kul.pl

Paweł Wójcik, PhD

Fields of interest: singular integrals, Faber Polynomials, approximation methods

Current research:

    • Dorota Pylak, Paweł Karczmarek, Paweł Wójcik. Approximate solution of a singular
      integral equation with a cauchy kernel on the euclidean plane. Computational Methods
      in Applied Mathematics, 18(4):741–752, 2018.

    • M. A. Sheshko, D. Pylak, P. Wójcik. Application of faber polynomials to the approximate
      solution of the riemann problem. Ukrainian Mathematical Journal, 68(12):1965–
      1974, May 2017.

    • Michail A Sheshko, Paweł Karczmarek, Dorota Pylak, Paweł Wójcik. Application of
      faber polynomials to the approximate solution of a generalized boundary value problem
      of linear conjugation in the theory of analytic functions.
      Computers & Mathematics
      with Applications, 67(8):1474–1481, 2014.

International cooperation

e-mail: wojcikpa [at] kul.pl