COMPARISON OF SOLVING A STIFF EQUATION ON A SPHERE BY THE MULTI-LAYER METHOD AND METHOD OF CONTINUING AT THE BEST PARAMETER
Journal Title: Современные информационные технологии и ИТ-образование - Year 2018, Vol 14, Issue 3
Abstract
A stiff equation, linked with the solution of singularly perturbed differential equations with the use of standard methods of numeral solutions of simple differential equations often lead to major difficulties. First difficulty is the loss of stability of the counting process, when small errors on separate steps lead to an increase in the systematic errors in general. Another difficulty is, directly linked with the first one, consists of the need of decreasing the integrating step by a lot, which leads to a major decrease in the time taken for the calculations. On an example of a boundary value problem for a differential equation of second power on a sphere, comparison of our two approaches of constructing approximate values are held. The first approach is connected with the construction of an approximate multi-layer solution of the problem and is based on the use of recurrent equalities, which come out from classical numeral methods to the interval of a non-constant length. As a result, a numeral, approximated solution is replaced with an approximate solution in form of a function, which is easier to use for adaptation, building a graph and other needs. The second approach is linked with the continuation of the solutions by the best parameter. This method allows us to decrease majorly the number of steps and increase the stability of the computing process compared to standard methods.
Authors and Affiliations
Elena Budkina, Evgenii Kuznetsov, Dmitriy Tarkhov, Anastasia Gomzina, Semyon Maltsev
Keywords
Related Articles
- EP ID EP515175
- DOI 10.25559/SITITO.14.201803.533-541
- Views 89
- Downloads 0
REFACTORING OF THE OPENVZ DRIVER FOR THE OPENNEBULA CLOUD PLATFORM WITHIN THE JINR CLOUD INFRASTRUCTURE PROJECT
This article explores the possibilities of using OpenVZ virtualization technology in the cloud infrastructure of the Joint Institute for Nuclear Research (JINR), built on the OpenNebula platform. OpenNebula is an open a...
WEB TECHNOLOGIES, ARTIFICIAL INTELLIGENCE AND COGNITIVE GOVERNMENT
It remains an open question whether the decentralized ecosystems distributed in the mobile environment of the fog computing system will eventually displace more centralized data development systems like Knowledge Vault a...
HARTLEY AND LKLB-PROCESS MEASURES: USE IN PSYCHOLOGICAL AND EDUCATIONAL TESTING
The problems of social analytics and decision-making on the management of complex information and economic structures are increasingly determined by human factors. The difficulty in regulating and recognizing information...
MULTIHEURISTIC APPROACH TO COMPARE THE QUALITY OF DEFINED METRICS ON THE SET OF DNA SEQUENCES
In this article, we analyzed some several metrics that determine the differences in DNA sequences of different species. Several standard metrics are considered, as well as a modification of the original author's metric,...
A METHOD OF CONSTRUCTING A BLOCK CIPHERS ROUND FUNCTION’S POLYNOMIAL OVER A FINITE FIELD
The work outlines the method of construction of round function as a polynomial of one variable over the finite field. The proposed method is based on the calculation of the initial cryptographic transformation at special...