@article{Gusynin_Gusynin_Tachinina_2016, title={THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS}, volume={69}, url={https://jrnl.nau.edu.ua/index.php/visnik/article/view/11054}, DOI={10.18372/2306-1472.69.11054}, abstractNote={<p><strong><em>Purpose: </em></strong><em>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. <strong>Methods: </strong>This article reviews two approaches</em><em> </em><em>based on differential transformations for solving non-linear boundary value problems: the modified differential transform method and the system-analogue simulation method.<strong> Results: </strong>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. <strong>Discussion: </strong>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.</em></p>}, number={4}, journal={Proceedings of National Aviation University}, author={Gusynin, Viacheslav and Gusynin, Andrii and Tachinina, Helen}, year={2016}, month={Dec.}, pages={44–55} }