Chapter 1. Solution of Differential Equations Systems that Arise During the Analysis of Complex Multicomponent Environments 1
V. BOHAIENKO, O. MARCHENKO and T. SAMOILENKO
1.1. Construction of an approximate solution of the axisymmetric parabolic problem 1
1.2. The analysis of numerical modeling of soil mass dynamics in the presence of unsteady pressure filtration 14
1.3. The analysis of numerical simulation of non-isothermal processes in soil 26
1.4. The study of soil massif state in the foundations of hydraulic structures 34
1.5. Parallel algorithm for AMLI preconditioner and its application to model soil massif state 46
1.6. References 68
Chapter 2. Computer Simulation of Transdermal Drug Delivery Using Soluble Microneedles 71
D.A. KLYUSHIN, S. LYASHKO, V.V. ONOTSKYI and O.S. BONDAR
2.1. Introduction 71
2.2. Mathematical model 72
2.3. Mathematical methods 78
2.4. Numerical experiments 80
2.5. Results and discussion 81
2.6. Conclusion 91
2.7. References 91
Chapter 3. Homogenization and Modeling of Processes in Composites Similar to Photonic Crystals 95
G.V. SANDRAKOV
3.1. Introduction 95
3.2. Composite media with periodic structures and contrast properties 98
3.3. Regular homogenized asymptotic expansions of solutions 100
3.4. Singular homogenized asymptotic expansions of solutions 107
3.5. Computational aspects of modeling by homogenization 117
3.6. Spectral aspects of modeling by homogenization 119
3.7. Conclusion 129
3.8. References 129
Chapter 4. Polynomial Operator Interpolation and its Applications 133
V.L. MAKAROV and O.F. KASHPUR
4.1. Introduction 133
4.2. Formulation of Lagrange's operator interpolation problem 135
4.3. Solution of the Lagrange's operator interpolation problem 136
4.4. Solution operator equations by the interpolation method 139
4.5. Interpolation in Euclidean spaces 143
4.6. Construction of surfaces 146
4.7. Conclusion 151
4.8. References 151
Chapter 5. New Fractional Differential Analogues of the Biparabolic Evolution Equation and Some Boundary Value Problems 155
V.M. BULAVATSKY and S. LYASHKO
5.1. Introduction 155
5.2. Some boundary value problems for the fractionalâ"differential analogue of the biparabolic equation with non-locality in time and space 159
5.3. Generalization of the model equation based on Hilfer-type fractional derivatives 169
5.4. Fractionalâ"differential analogue of the biparabolic evolution equation with Caputo and Caputoâ"Fabrizio derivatives 173
5.5. Conclusions 178
5.6. References 178
Chapter 6. Optimal Control for Integro-differential Systems of Hyperbolic Type 181
A.V. ANIKUSHYN, Kh.M. HRANISHAK, V.S. LYASHKO and O.S. BONDAR
6.1. Introduction 181
6.2. Main notations and spaces 189
6.3. Generalized control problem 191
6.4. A priori inequalities for the differential part of the operator 197
6.5. A priori inequalities for the integro-differential operator 205
6.6. Example of an optimal control problem 212
6.7. Conclusion 219
6.8. References 219
Chapter 7. Self-adaptive Operator Extrapolation Method for Operator Inclusions in Banach Space 223
V. SEMENOV and S. DENYSOV
7.1. Introduction 223
7.2. Preliminaries 227
7.3. Algorithm 231
7.4. Convergence 233
7.5. Variants 239
7.6. Application to variational inequalities 241
7.7. Conclusion 243
7.8. Acknowledgments 243
7.9. References 243
Chapter 8. Forecasting Algorithms Based on Intellectual Analysis of Polynomial Extrapolation and Divided Differences 247
Y. TURBAL, M. TURBAL and A. BOMBA
8.1. Introduction â" Problem of the time series forecasting 247
8.2. Method of finding the predictive value based on a polynomial of any degree without finding the coefficients of the polynomial 249
8.3. The optimal polynomial extrapolation problem 254
8.4. Condition of forecast efficiency based on the arithmetic mean of polynomial forecasts 260
8.5. Improved algorithm for optimal polynomial forecasting 262
8.6. Numerical results of the polynomial forecast 266
8.7. Pyramidal method of extrapolation 271
8.8. Numerical results for the pyramidal methods 283
8.9. Conclusions 285
8.10. References 286
Chapter 9. Transformer with BPE Tokenization for Analysis of Interactions of Chemical Substances and Proteins 289
M. ZOZIUK, P. KRYSENKO, S. DOVGIY, V. MAKAROV, Y. YAKIMENKO and D. KOROLIOUK
9.1. Introduction 290
9.2. Methods and data 291
9.3. The model's architecture 293
9.4. The model's training 295
9.5. Conclusion 298
9.6. References 298
List of Authors 301
Index 305
