This book presents an overview of the most recent research and findings in the field of approximation and regularisation methods for operator-functional equations, and explores their applications in electrical and power engineering. It presents the state of the art in building operator theory, regularised numerical methods, and the verification of mathematical models for dynamical models based on integral and differential equations. Special attention is paid to Volterra models, a powerful tool for modelling hereditary dynamics.
This book begins by exploring the solvability of singular integral equations and moves on to study approximation methods for linear operator equations and nonlinear integral equations. Following this, it examines loaded equations and bifurcation analysis, before concluding with an investigation of the applications of the contents of the book in electrical engineering and automation. Each chapter provides an overview and analysis of the relevant problem statements, outlines current methods within the field, and identifies future directions for research.
With an interdisciplinary approach, this book is essential reading for anyone interested in operator-functional equations. Graduate students and professors in the fields of applied mathematics, physics, materials science, and numerical analysis will find this work insightful and valuable, as will industry professionals in related fields.
Contents:
- Introduction
- Solvability of Singular Integral Equations on Banach Function Spaces
- Approximation Methods for Linear Operator Equations and Nonlinear Integral Equations
- Loaded Equations and Bifurcation Analysis
- Applications in Electrical Engineering and Automation
Readership: This book is suitable for both graduate students and professors in applied mathematics, physics, material science, and numerical analysis. It is also suitable for industry professionals in the fields of electrical and thermal engineering, combustion, and biomass.
'This book offers new ideas, tools, and models that can be used by applied mathematicians and engineers to solve practical problems in electrical engineering. It also demonstrates how theories such as singular integrals, functional equations, stochastic arithmetic, and fixed point theorems can be applied by pure mathematicians and theoretical physicists in the study of linear and nonlinear equations within integral dynamical models.' - Professor Yang Jiazhong School of Mathematical Sciences, Peking University, China
