APPROXIMATION AND REGULARISATION METHODS FOR OPERATOR-FUNCTIONAL EQUATIONS

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.

Denis Sidorov (DSc, PhD) was born in Irkutsk, Russia, in 1974. He is currently Chair Professor of Harbin Institute of Technology and Principal Researcher with both the Melentiev Energy Systems Institute and Irkutsk National Research Technical University. He served as Distinguished Guest Professor of Hunan University (PRC) and Queen's University Belfast (UK) between 2016 and 2020. Professor Sidorov was an elected Chapter Chair of IEEE Power and Energy Society Russia (Siberia) between 2018 and 2022. He serves on the editorial boards of Renewable and Sustainable Energy Reviews and Renewable Energy. He has authored more than 140 scientific papers and four monographs. His research interests include integral and differential equations, machine learning, wind energy, and inverse problems.

Edixon Rojas (PhD) was born in Venezuela in 1978. He is currently an associate professor with the Department of Mathematics at the National University of Colombia, and was an assistant professor with the Department of Mathematics at Xavierian Pontifical University (Bogotá, Colombia) between 2011 and 2014. He received his PhD from the University of Aveiro in Portugal in 2010, is the author of 50 research papers, and has delivered more than 20 talks in international conferences. His scientific interests include: operator theory, singular and non-linear integral equations, ordinary differential equations, non-linear functional analysis and function spaces.

Alexander Sinitsyn (DSc, PhD) was born in Irkutsk, Russia, in 1961. He is currently a professor at the National University of Colombia. He has been a visiting professor at a number of leading research institutions, including Paul Sabatier University (1995, 1996, 2000), the Department of Mathematics at the Ludwig Maximilian University of Munich (2000), the Erwin Schrödinger International Institute for Mathematics and Physics (2000), the Institute of Mathematics at the Chinese Academy of Sciences (2009, 2018), and the Technion - Israel Institute of Technology (2009, 2018). Professor Sinitsyn won the European INTAS grant in 2000 with Prof. P Degond and Prof. P Markowich. His research interests include: partial and ordinary differential equations, asymptotics, stability, qualitative properties of Vlasov-Maxwell systems, boundary value problems for semilinear nonlocal elliptic equations; steady-state and nonstationary solutions of Vlasov-Maxwell-Fokker-Planck systems, applications to earthquake source modeling.

Nikolai Sidorov (DSc, PhD) was born in Irkutsk, Russia, in 1940. He serves as Chair Emeritus Professor of mathematical analysis and differential equations at Irkutsk State University. He has been invited to talk at ICIAM congresses, and has served as guest professor at Warwick University, Cambridge University, Chalmers University, Fudan University, Edinburgh University, the Engineering University of Hamburg, and the Banach Mathematical Centre in Warsaw. Professor Sidorov has also been awarded the title of Honoured Scientist of Russia. His scientific interests include: branching of solutions of the nonlinear equations, the bifurcation theory, singular boundary value problems, regularization and approximate methods, the differential-operator equations and kinetic systems.