THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS
Journal Title: Вісник Національного Авіаційного Університету - Year 2016, Vol 69, Issue 4
Abstract
Purpose: The aim of our study is comparison of method applications based on differential transformations for solving boundary value problems which are described by non-linear ordinary differential equations. Methods: This article reviews two approaches based on differential transformations for solving non-linear boundary value problems: the modified differential transform method and the system-analogue simulation method. Results: In this paper, we present results of the numerical solution of non-linear boundary value problem by methods based on differential transformations for demonstration the effectiveness and applicability of techniques. The relative error for given solutions, obtained with using first 6 discretes of differential spectra is presented. Discussion: Comparison of numerical solutions obtained by modified differential transform method and system-analogue simulation method with exact solution shows that both methods have good agreement with exact solution of non-linear boundary value problem for small intervals. However, application of system-analogue simulation method is preferential for big intervals, on which the boundary value problem is solved.
Authors and Affiliations
Viacheslav Gusynin, Andrii Gusynin, Helen Tachinina
Keywords
Related Articles
- EP ID EP460956
- DOI 10.18372/2306-1472.69.11054
- Views 110
- Downloads 0
APPLICATION OF MISTLETOE IN CANCER TREATMENT
Objective: natural method of cancer treatment with the he lp of Viscum AlBum is described in the article. Chemical composition, application of mistletoe in medicine and influence on cell li...
LEGISLATIVE COLLISIONS OF LEGAL REGULATION OF ADMINISTRATIVE ENFORCEMENT WITHIN ACTIVITIES OF NATIONAL BANK OF UKRAINE AND METHODS OF THEIR ELIMINATION
Purpose: Determining legislative conflicts and gaps related to imposing sanctions by the National Bank of Ukraine to banks as well as developing the grounded o ffers on how to eliminate the respective le...
PULSE CHARACTERISTICS OF NETWORK SATELLITE SYSTEMS ADAPTIVE ANTENNA FOR ASSESSING CORRELATION INTERFERENCE MATRIX
Purpose: On the basis of spatial filtering, we propose a method for direct calculation of the inverse correlation interference matrix with unknown parameters of the input action for controlling the pattern of the adaptiv...
MATHEMATICAL MODEL OF UNMANNED AERIAL VEHICLE CONTROL IN SINGLE CONTROL CHANNEL
The main aim of this research is development of the mathematical model. Developed model will allow deeper, qualitative and faster selection of the proper values of coefficients that are necessary for optimal and effectiv...
SYSTEM OF GUARANTEED RESOLUTION OF DYNAMIC CONFLICTS OF AIRCRAFTS IN REAL TIME
Purpose: The present work is devoted to improving of flight safety in civil aviation by creating and implementing a new system of resolution of dynamic conflict of aircrafts. The developed system is aimed at ensuring a g...