Abstract: We review the development of the infinity concept and continuous mathematics from ancient times to the present day. To the critical analysis of the application of the infinitesimal in the mathematical modeling in XVIIXVIII centuries is given special attention. It is noted necessity of development methods for the analysis of finite small disturbances in computer simulations. The problem of the adequacy of the linear approximation of mathematical and computer models is under discussion. We investigate the influence of finite small disturbances into elements of model to quality of localization solutions of the model which is based on the methodology of options sequential analysis. The results of numerical experiments and taken into account the level of systems conditionality and algorithms (the mantissa length in the numbers representation) are given.

Keywords: continuous and infinite, infinitesimal analysis, mathematical and computer simulation, linear approximation, localization, successive analysis variants, analysis finitely small values

ACM Classification Keywords: H.4.2 Information Systems Applications: Types of Systems: Decision Support.

Link:

ANALYSIS FINITELY SMALL VALUES IN COMPUTER SIMULATION

Oleksii Voloshyn, Vladimir Kudin

http://www.foibg.com/ijima/vol03/ijima03-03-p01.pdf