THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS

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

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  • EP ID EP460956
  • DOI 10.18372/2306-1472.69.11054
  • Views 136
  • Downloads 0

How To Cite

Viacheslav Gusynin, Andrii Gusynin, Helen Tachinina (2016). THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS. Вісник Національного Авіаційного Університету, 69(4), 44-55. https://europub.co.uk/articles/-A-460956