Mathematical Models and Integration Methods

Seminar Proceedings on Applications to Mechanics and Physics

Oleg V. Kaptsov, Evgeniy I. Kaptsov

• Publisher: De Gruyter
• Year: 2024
• Topic: Mathematics
• eBook ISBN:
  9783111546803
• Subtopic: Applied Mathematics
• Index: Mathematics

The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods. It covers classical and contemporary integration techniques for partial differential equations, including Monge and Darboux's approaches and their extensions. Additionally, it introduces a novel theoretical model for plane turbulent flows, presents gravitational equations derived from the principle of least action, and explores symmetry-preserving conservative finite-difference schemes for hydrodynamic-type equations. Analytical solutions for Maxwell's equations in incompressible viscoelastic mediums are examined, alongside theoretical-group analysis of wake mathematical models and reduction to ordinary differential equations. The book also delves into special classes of two-dimensional ideal fluid motion and advancements in discrete orthogonal polynomial theory, showcasing rapid decay properties near interval boundaries. In conclusion, this comprehensive collection is indispensable for researchers and practitioners in applied mathematics, fluid dynamics, and computational modeling, providing valuable insights into cutting-edge methods and solutions in the field.

Table of contents

• Title Page
• Copyright
• Contents
• Intermediate systems and invariants
• Folding in fluids
• Vortex models of plane turbulent flows
• Equations of dyon electromagnetic field
• Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points
• Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations
• On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium
• Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake
• Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid
• Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters
• Subject Index