DIFFERENTIAL TRANSFORM METHOD FOR SOLVING NON-LINEAR DIFFERENTIAL EQUATIONS BY THE ADOMIAN POLYNOMIALS
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2017, Vol 1, Issue 104
Abstract
Purpose. The aim of our study is to consider a novel approach for solving science and engineering problems are described by non-linear ordinary differential equations. Results and originality. The given approach consists in the joint use of the differential transform method and the method of Adomian polynomials. The main idea of proposed method based on solving equations in the image field with approximation of non-linear terms of differential equation by corresponding Adomian polynomials and henceforth obtaining of original of solution as a Taylor series. The proposed approach allows to overcome the mathematical obstacles during differential image calculation of complex non-linearities and essentially reduce the computational cost during searching of approximate solution of non-linear differential equation. Practical value. The proposed approach widens the application of differential transform method to deal with non-linear differential equations with different types of nonlinearity due to the properties and available algorithms of the Adomian polynomials. Numerical experiments demonstrate the application effectiveness of the proposed approach for solving non-linear differential equations and the good agreement with exact solution.
Authors and Affiliations
A. Gusynin
Keywords
Related Articles
- EP ID EP659599
- DOI -
- Views 80
- Downloads 0
INCREASING THE ACCURACY OF COMPOSITES MECHANICAL PROPERTIES DETERMINATION BASED ON CARBON FIBERS USING RATIONAL PROCESSING METHODS
Purpose. To prove increasing the accuracy of the carbon-carbon composites mechanical properties determination using rational methods of samples processing. Methodology. The comparative analysis method has been used to fi...
THE LOCAL SELF-GOVERNMENT AUTHORITIES ROLE IN ACTIVATION OF FOREIGN ECONOMIC ACTIVITY OF THE ENTERPRISES
Purpose. The goal of the article is analysis of the theoretical approaches of the local self-government authorities to the foreign economic activity, investigating of the local self-government authorities’ competence in...
BORROWINGS IN JOURNALISTIC TEXT AS A FACTOR OF STUDENTS’ SOCIAL AND CULTURAL COMPETENCE EXPANSION
Purpose. Research of the borrowings in a journalistic text and the way they can influence the valuation of stu- dents’language competence are the relevant task. Methodology. analytical research, semantic, etymologic...
MATHEMATICAL MODELING OF THE EXTERNAL FACTORS INFLUENCE ON THE MARGIN OF STRENGTH WHILE SHAFT SINKING
Purpose. To improve structural and technological parameters of vertical shafts as an important issue in coal industry. To estimate the margin of strength of the vertical shaft lining considering the change of its thickne...
IMPROVING THE QUALITY OF ABRASIVE CUTTING CARBON-CARBON COMPOSITES THROUGH RATIONAL CONDITIONS OF DYNAMIC CONTACT
Purpose. Aspects of the processing of carbon-carbon materials with abrasive-containing rotational tools are considered. It is shown that to ensure the high quality of the surfaces obtained, it is necessary to take into a...