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

Authors

  • Viacheslav Gusynin Acting General Director Ukraine, Binational company «Alc?ntara Cyclone Space»
  • Andrii Gusynin National Technical University of Ukraine «Igor Sikorsky KPI»
  • Helen Tachinina National Aviation University

DOI:

https://doi.org/10.18372/2306-1472.69.11054

Keywords:

Adomian polynomials, differential transformations, modified differential transform method, non-linear boundary value problem, system-analogue simulation method

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.

Author Biographies

Viacheslav Gusynin, Acting General Director Ukraine, Binational company «Alc?ntara Cyclone Space»

Doctor of Engineering

Acting General Director Ukraine, Binational company «Alc?ntara Cyclone Space»

Education: Taras Shevchenko National University of Kyiv, Kyiv, Ukraine (1973).

Research area: flight dynamics, optimal control, differential transformation.

Andrii Gusynin, National Technical University of Ukraine «Igor Sikorsky KPI»

Candidate of Engineering, Associate Professor.

Associate Professor, National Technical University of Ukraine «Igor Sikorsky KPI»

Education: International Solomon University, Kyiv, Ukraine (2000).

Research area: flight dynamics, automatization, optimal control, differential transformation.

Helen Tachinina, National Aviation University

Candidate of Engineering, Associate Professor.

Department of Automation and Energy Management, National Aviation University

Education: National Aviation University, Kyiv, Ukraine (2000).

Research area: flight dynamics, automatization, optimal control.

References

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Published

21-12-2016

How to Cite

Gusynin, V., Gusynin, A., & Tachinina, H. (2016). THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS. Advances in Aerospace Technology, 69(4), 44–55. https://doi.org/10.18372/2306-1472.69.11054

Issue

Section

AEROSPACE SYSTEMS FOR MONITORING AND CONTROL