This book is based on the best papers accepted for presentation during the International Conference on Actual Problems of Applied Mathematics and Computer Systems (APAMCS-2022), Russia. The book includes research materials on modern mathematical problems, solutions in the field of scientific computing, data analysis and modular computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in data analysis and modular computing include contributions in the field of deep learning, neural networks, mathematical statistics, machine learning methods, residue number system and artificial intelligence. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of scientific computing, parallel computing, computer technology, machine learning, information security and mathematical education.

Includes research materials on modern mathematical problems and solutions in the field of scientific computing Results from the International Conference on Actual Problems of Applied Mathematics and Computer Systems (APAMCS-2022) Written by experts in the field

Autorentext

Anatoly Alikhanov has obtained his Ph.D. in Physical and Mathematical Sciences and is Vice-Rector for Scientific and Research work of the North Caucasus Federal University. He is the Head of the Regional Scientific and Educational Mathematical Center "North Caucasian Center for Mathematical Research." Earlier, he worked as Visiting Member of the dissertation council at Southeast University, Department of Mathematics, Nanjing, China. In 2016, he was invited for an internship in the field of numerical methods for solving fractional differential equations at the Nanjing University of China. . Alikhanov is Member of the Editor Board of the Fractional Calculus and Applied Analysis Journal and Reviewer of over 30 reputable scientific journals in computational mathematics.

Pavel Lyakhov graduated in mathematics in Stavropol State University, in 2009, where he also received the Ph.D. degree in computer science, in 2012. He has been working at North-Caucasus Federal University, since 2012. He is currently the Head of the Department of Mathematical Modeling, North-Caucasus Federal University. His research interests include high-performance computing, quantum computing, residue number systems, digital signal processing, image processing and machine learning.

Irina Samoylenko, PhD, Associate Professor at Informational Systems Department, Stavropol State Agrarian University, Russia. She received M.S. degree in Applied Mathematics and Informatics, PhD in System Analysis, Control and Processing of Information in North-Caucasus Federal University. Irina is a researcher in North-Caucasus Centre for Mathematical Research, North-Caucasus Federal University. She is a member of Association of Scientific Editors and Publishers, Russia. Her research interests include wireless sensor networks, IoT, optimization tasks and mathematical modeling.

Inhalt
Modeling of the potential dependence on the permittivity at the metal dielectric medium interface.- Difference method for solving the Dirichlet problem for a multidimensional integro-differential equation of convection-diffusion.- The problem of restoring the unit of approximation in the model for studying functional dependence from approximate data.- RNS Reverse conversion algorithm and parity detection for the wide arbitrary moduli set.- Anomalous solute transport in an inhomogeneous porous medium taking into account mass transfer.- Determination of relaxation and flow coefficients during filtration of a homogeneous liquid in fractured-porous media.- Solution of the anomalous filtration problem in two-dimensional porous media.- On calculating the hyperbolic parameter of a two-dimensional lattice of linear comparison solutions.- Numerical solution of anomalous solute transport in a two-zone fractal porous medium.- Initial-boundary value problems for the loaded Hallaire equation withGerasimovCaputo fractional derivatives of different orders. <p