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.