Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 2

Dmitri Koroliouk is a Professor at the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine.Sergiy Lyashko is Head of the Department of Computational Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.Nikolaos Limnios is a Professor at the Sorbonne University Alliance, Université de Technologie de Compiègne, France.

• Chapter 1. Solution of Differential Equations Systems that Arise During the Analysis of Complex Multicomponent Environments 1V. BOHAIENKO, O. MARCHENKO and T. SAMOILENKO1.1. Construction of an approximate solution of the axisymmetric parabolic problem 11.2. The analysis of numerical modeling of soil mass dynamics in the presence of unsteady pressure filtration 141.3. The analysis of numerical simulation of non-isothermal processes in soil 261.4. The study of soil massif state in the foundations of hydraulic structures 341.5. Parallel algorithm for AMLI preconditioner and its application to model soil massif state 461.6. References 68Chapter 2. Computer Simulation of Transdermal Drug Delivery Using Soluble Microneedles 71D.A. KLYUSHIN, S. LYASHKO, V.V. ONOTSKYI and O.S. BONDAR2.1. Introduction 712.2. Mathematical model 722.3. Mathematical methods 782.4. Numerical experiments 802.5. Results and discussion 812.6. Conclusion 912.7. References 91Chapter 3. Homogenization and Modeling of Processes in Composites Similar to Photonic Crystals 95G.V. SANDRAKOV3.1. Introduction 953.2. Composite media with periodic structures and contrast properties 983.3. Regular homogenized asymptotic expansions of solutions 1003.4. Singular homogenized asymptotic expansions of solutions 1073.5. Computational aspects of modeling by homogenization 1173.6. Spectral aspects of modeling by homogenization 1193.7. Conclusion 1293.8. References 129Chapter 4. Polynomial Operator Interpolation and its Applications 133V.L. MAKAROV and O.F. KASHPUR4.1. Introduction 1334.2. Formulation of Lagrange's operator interpolation problem 1354.3. Solution of the Lagrange's operator interpolation problem 1364.4. Solution operator equations by the interpolation method 1394.5. Interpolation in Euclidean spaces 1434.6. Construction of surfaces 1464.7. Conclusion 1514.8. References 151Chapter 5. New Fractional Differential Analogues of the Biparabolic Evolution Equation and Some Boundary Value Problems 155V.M. BULAVATSKY and S. LYASHKO5.1. Introduction 1555.2. Some boundary value problems for the fractional–differential analogue of the biparabolic equation with non-locality in time and space 1595.3. Generalization of the model equation based on Hilfer-type fractional derivatives 1695.4. Fractional–differential analogue of the biparabolic evolution equation with Caputo and Caputo–Fabrizio derivatives 1735.5. Conclusions 1785.6. References 178Chapter 6. Optimal Control for Integro-differential Systems of Hyperbolic Type 181A.V. ANIKUSHYN, Kh.M. HRANISHAK, V.S. LYASHKO and O.S. BONDAR6.1. Introduction 1816.2. Main notations and spaces 1896.3. Generalized control problem 1916.4. A priori inequalities for the differential part of the operator 1976.5. A priori inequalities for the integro-differential operator 2056.6. Example of an optimal control problem 2126.7. Conclusion 2196.8. References 219Chapter 7. Self-adaptive Operator Extrapolation Method for Operator Inclusions in Banach Space 223V. SEMENOV and S. DENYSOV7.1. Introduction 2237.2. Preliminaries 2277.3. Algorithm 2317.4. Convergence 2337.5. Variants 2397.6. Application to variational inequalities 2417.7. Conclusion 2437.8. Acknowledgments 2437.9. References 243Chapter 8. Forecasting Algorithms Based on Intellectual Analysis of Polynomial Extrapolation and Divided Differences 247Y. TURBAL, M. TURBAL and A. BOMBA8.1. Introduction – Problem of the time series forecasting 2478.2. Method of finding the predictive value based on a polynomial of any degree without finding the coefficients of the polynomial 2498.3. The optimal polynomial extrapolation problem 2548.4. Condition of forecast efficiency based on the arithmetic mean of polynomial forecasts 2608.5. Improved algorithm for optimal polynomial forecasting 2628.6. Numerical results of the polynomial forecast 2668.7. Pyramidal method of extrapolation 2718.8. Numerical results for the pyramidal methods 2838.9. Conclusions 2858.10. References 286Chapter 9. Transformer with BPE Tokenization for Analysis of Interactions of Chemical Substances and Proteins 289M. ZOZIUK, P. KRYSENKO, S. DOVGIY, V. MAKAROV, Y. YAKIMENKO and D. KOROLIOUK9.1. Introduction 2909.2. Methods and data 2919.3. The model's architecture 2939.4. The model's training 2959.5. Conclusion 2989.6. References 298List of Authors 301Index 305