Differential Equations, Mathematical Modeling and Computational Algorithms

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Illuminates modern mathematical problems New mathematical and numerical methods New mathematical models

Inhalt

V. E. Fedorov and K. V. Boyko, Some Classes of Quasilinear Equations with Gerasimov - Caputo Derivatives.- A. Glushak, On the Solvability of Initial Problems for Abstract Singular Equations Containing Fractional Derivatives.- A. Kulikov and D. Kulikov, Local Bifurcations of Periodic Traveling Waves in the Generalized Weakly Dissipative Ginzburg-Landau Equation.- R. Soren Kraußhar, A. Legatiuk, and D. Legatiuk, Towards discrete octonionic analysis.- Igor S. Lomov, Axiomatic method for constructing a generalized solution of a mixed problem for a telegraph equation.- A. Mironov and L. Mironova, "Non-local Substitutions for Liouville Equations with Three and Four Independent Variables.- Li Liu, Zhenbin Fan, Gang Li, and Sergey Piskarev, Convergence rates of a finite difference method for the fractional subdiffusion equations.- M. Plekhanova and E. Izhberdeeva, Degenerate quasilinear equations with Dzhrbashyan Nersesian derivatives and applications.- Marina V. Polovinkinaand Igor P. Polovinkin, On a K-homogeneous metric.- F. Sadyrbaev, I. Samuilik, and V. Sengileyev, Biooscillators in models of genetic networks.- A. Setukha and S. Stavtsev, Numerical Method for Problem of Scattering by a Small Thickness Dielectric Layer on a Perfectly Conductive Substrate.- Maxim V. Shamolin, Invariants of Dynamical Systems with Dissipation on Tangent Bundles of Low-Dimensional Manifolds.- E. Shishkina, B-subharmonic functions.- S. M. Sitnik, V. Skoromnik and M. V. Papkopvich, Some Multi-Dimensional Modied G- and H-Integral Transforms on Spaces.- B.D. Koshanov and A.P. Soldatov, On sufficient conditions of the Faddeev-Marchenko theorem.- N. Subbotina and E. Krupennikov, Variational approach to construction of piecewise-constant approximations of the solution of dynamic reconstruction problem.- A. Vasilyev, V. Vasilyev, and Asad Esmatullah, Discrete Operators and Equations: Analysis and Comparison.- V. Vasilyev, V. Polunin and I. Shmal, Pseudo-Differential Equations in Spaces of Different Smoothness Exponents on Variables.- Yuri P. Virchenko, Thermodynamic limit in vector lattice models.- N. V. Zaitseva, Family of smooth solutions of a hyperbolic differential-difference equation.