Forming a мetodology for transforming a model as the basis for expanding its informativeness
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2019, Vol 5, Issue 4
Abstract
<p>A problem on building the methodology for transforming the implicit form of a model has been stated and solved, which improves the efficiency of replacing complex nonlinear forms of mathematical models to reducing them to a recurrent sequence in the form of analytical expressions that allow quick express calculations.</p><p>New explicit forms of the models have been proposed that make it possible to use recurrent sequences for representing a solution to the problem and forming an error estimation expression, as well as and additional information. Given the fact that for many attributes the solution and an error estimation are critical, the analyticity of expressions reveals new properties and possibilities. Based on such factors as authenticity, accuracy, depth, materiality and completeness, the adequacy of the model is represented by a single analytical expression that would make it possible in future to simplify the process of comparison through the use of quantitative methods. Representation of transformations, according to which the connection between the error of two consecutive approximations and dependence on the approximation number was established, is predetermined by the necessity to analyze convergence dynamics based on the iteration number. Another variant, not less important, which can characterize the dynamics of convergence is the connection between an error of the first approximation and the arbitrary approximation. Based on the overall expansion of the implicit form of the model and the mean value theorem, the relationship between the two consecutive errors or norms has been established. It is demonstrated that if the error or a norm of error are assigned, the estimates for the first and second derivatives would make it possible to determine the boundary number of the iteration starting from which the error is less than the assigned one.</p><p>An example has been given for deriving an estimation for the general model of the magnitude of a maximally possible error, the boundary number of the iteration, starting from which the error acquires a value less than the assigned one. A comprehensive analytical assessment of adequacy based on a single expression has also been derived.</p><p>Representation of informational attributes in the quantitative form is predetermined by new opportunities that would emerge due to the obtained tools for quantitative analysis.</p><p>Numerical modelling has been performed; the character of dynamics of new informational indicators and attributes has been examined. The data given for nine iterations demonstrate efficiency and completeness of information to perform a quick analysis and draw a conclusion. Based on the dynamics of quantitative attributes for a relative error, as well as new ones, proposed based on the results from implementing the model transformation methodology, it has been shown that the possibilities emerge to run a quick analysis and draw a conclusion. It was demonstrated that the introduced attributes expand the informativeness of the methodology implementation for the further representation of a nonlinear model in the form of a recurrent sequence</p>
Authors and Affiliations
Alexander Trunov
Keywords
Related Articles
- EP ID EP668811
- DOI 10.15587/1729-4061.2019.181866
- Views 84
- Downloads 0
Determination of parameters of the stochastic inventory management system in the conditions of economically-based shortage
<p>A methodical approach to determining the optimal parameters of a stochastic inventory management system in the context of an economically justified deficit that allows responding quickly to fluctuations in demand and...
Determining rational parameters of the capacitive energy storage system for the underground railway rolling stock
<p>An approach was proposed for determining rational parameters of the on-board capacitive energy storage for the underground railway rolling stock with recuperation systems. The essence of the approach is to determine t...
Motion equations of the singlemass vibratory machine with a rotaryoscillatory motion of the platform and a vibration exciter in the form of a passive autobalancer
<p>This paper describes a mechanical model of the single-mass vibratory machine with a rotary-oscillatory motion of the platform and a vibration exciter in the form of a passive auto-balancer. The platform can oscillate...
Establishing temperature and time factors for the post-pasteurization of gourmet meat products
<p>Conditions of post-pasteurization of whole-muscle gourmet meat products have been developed. They make it possible to extend shelf life of the product without change of its organoleptic characteristics.</p><p>Effect o...
Substantiation of the development of formulations for organic cupcakes with an elevated protein content
<p class="a">In order to develop the formulations for organic cupcakes with an elevated protein content, we examined and analyzed the amino acid composition of four samples of flour: wheat flour, organic wheat flour, org...