Cambridge Scholars Publishing Synthesis of Adequate Mathematical Descriptions of Physical Processes

For effective use of the results of computational calculations, it is necessary that the computational schemes used correspond to real physical processes, so that the schemes are adequate. The issue of adequacy is currently poorly understood and there are also no generally accepted criteria of adequacy. This book is the first to address the questions of constructing adequate mathematical descriptions of physical processes and their reasonable use in the future for various purposes. It proposes two adequacy criteria (quantitative and qualitative), and describes several possible algorithms for synthesis of cases when the physical process is composed of a system of ordinary differential equations or a mathematical model in algebraic form. The algorithms described here will be useful for specialists in areas where methods of mathematical modeling are used, such as mechanics. About the Author Yuri Menshykov, DSc, is a Senior Researcher and Associate Professor in the Department of Differential Equations at Dnipro University, Ukraine. He was educated at Kharkov and Dnepropetrovsk Universities, and defended his thesis in 1978. He has around 400 scientific publications to his credit, including chapters in Robotics, Automation and Control (2008) and Modeling and Simulation in Engineering (2019), and the book Identification of Models of External Loads (2009). One of his most important articles is “Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems”, published in the European Journal of Mathematical Sciences (2013).