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Computational methods and mathematical modeling in cyberphysics and engineering applications. 2 /

Situated at the intersection of advanced applied mathematics, computational science and engineering modeling, Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 2 presents contemporary analytical and numerical approaches to complex multiscale systems. This b...

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Bibliographic Details
Other Authors: Koroliouk, Dmitri (Editor), Lyashko, Sergiy (Editor), Limnios, N. (Nikolaos) (Editor)
Format: eBook
Language:English
Published: London, UK : Hoboken, NJ : ISTE Ltd ; John Wiley & Sons, Inc., 2026.
Series:Sciences. Mathematics. Mathematics in engineering
Subjects:
Computer-aided engineering.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Chapter 1. Solution of Differential Equations Systems that Arise During the Analysis of Complex Multicomponent Environments
  • 1.1. Construction of an approximate solution of the axisymmetric parabolic problem
  • 1.2. The analysis of numerical modeling of soil mass dynamics in the presence of unsteady pressure filtration
  • 1.3. The analysis of numerical simulation of non-isothermal processes in soil
  • 1.4. The study of soil massif state in the foundations of hydraulic structures
  • 1.5. Parallel algorithm for AMLI preconditioner and its application to model soil massif state
  • 1.6. References
  • Chapter 2. Computer Simulation of Transdermal Drug Delivery Using Soluble Microneedles
  • 2.1. Introduction
  • 2.2. Mathematical model
  • 2.3. Mathematical methods
  • 2.4. Numerical experiments
  • 2.5. Results and discussion
  • 2.6. Conclusion
  • 2.7. References
  • Chapter 3. Homogenization and Modeling of Processes in Composites Similar to Photonic Crystals
  • 3.1. Introduction
  • 3.2. Composite media with periodic structures and contrast properties
  • 3.3. Regular homogenized asymptotic expansions of solutions
  • 3.4. Singular homogenized asymptotic expansions of solutions
  • 3.5. Computational aspects of modeling by homogenization
  • 3.6. Spectral aspects of modeling by homogenization
  • 3.7. Conclusion
  • 3.8. References
  • Chapter 4. Polynomial Operator Interpolation and its Applications
  • 4.1. Introduction
  • 4.2. Formulation of Lagrange's operator interpolation problem
  • 4.3. Solution of the Lagrange's operator interpolation problem
  • 4.4. Solution operator equations by the interpolation method
  • 4.5. Interpolation in Euclidean spaces
  • 4.6. Construction of surfaces
  • 4.6.1. Example
  • 4.6.2. Example
  • 4.6.3. Example
  • 4.7. Conclusion
  • 4.8. References.
  • Chapter 5. New Fractional Differential Analogues of the Biparabolic Evolution Equation and Some Boundary Value Problems
  • 5.1. Introduction
  • 5.2. Some boundary value problems for the fractional-differential analogue of the biparabolic equation with non-locality in time and space
  • 5.3. Generalization of the model equation based on Hilfer-type fractional derivatives
  • 5.4. Fractional-differential analogue of the biparabolic evolution equation with Caputo and Caputo-Fabrizio derivatives
  • 5.5. Conclusions
  • 5.6. References
  • Chapter 6. Optimal Control for Integro-differential Systems of Hyperbolic Type
  • 6.1. Introduction
  • 6.2. Main notations and spaces
  • 6.3. Generalized control problem
  • 6.4. A priori inequalities for the differential part of the operator
  • 6.5. A priori inequalities for the integro-differential operator
  • 6.6. Example of an optimal control problem
  • 6.7. Conclusion
  • 6.8. References
  • Chapter 7. Self-adaptive Operator Extrapolation Method for Operator Inclusions in Banach Space
  • 7.1. Introduction
  • 7.2. Preliminaries
  • 7.3. Algorithm
  • 7.4. Convergence
  • 7.5. Variants
  • 7.6. Application to variational inequalities
  • 7.7. Conclusion
  • 7.8. Acknowledgments
  • 7.9. References
  • Chapter 8. Forecasting Algorithms Based on Intellectual Analysis of Polynomial Extrapolation and Divided Differences
  • 8.1. Introduction
  • Problem of the time series forecasting
  • 8.2. Method of finding the predictive value based on a polynomial of any degree without finding the coefficients of the polynomial
  • 8.3. The optimal polynomial extrapolation problem
  • 8.4. Condition of forecast efficiency based on the arithmetic mean of polynomial forecasts
  • 8.5. Improved algorithm for optimal polynomial forecasting
  • 8.6. Numerical results of the polynomial forecast
  • 8.7. Pyramidal method of extrapolation.
  • 8.8. Numerical results for the pyramidal methods
  • 8.9. Conclusions
  • 8.10. References
  • Chapter 9. Transformer with BPE Tokenization for Analysis of Interactions of Chemical Substances and Proteins
  • 9.1. Introduction
  • 9.2. Methods and data
  • 9.3. The model's architecture
  • 9.4. The model's training
  • 9.5. Conclusion
  • 9.6. References
  • List of Authors
  • Index
  • EULA.