ESTIMATE OF ACCURACY OF APPROXIMATE SOLUTIONS OF NON-LINEAR BOUNDARY VALUE PROBLEMS BY THE MULTI-STEP DIFFERENTIAL TRANSFORM METHOD
Journal Title: Вісник Національного Авіаційного Університету - Year 2017, Vol 70, Issue 1
Abstract
Purpose: The present paper is aimed at estimating of accuracy and justification the application effectiveness of the multi-step differential transform method for solving non-linear boundary value problems. Methods: This article reviews the multi-step differential transform method for solving non-linear boundary value problem. Results: The upper bound of estimate of accuracy of approximate solutions of non-linear boundary value problems by the multi-step differential transform method for the case of accounting of restricted quantity of discretes of differential spectra is offered. We present results of numerical solution of a non-linear boundary value problem and shown the efficiency of application of the multi-step differential transform method compared with traditional differential transform method. Discussion: It is shown, that upper bound of error estimate of the multi-step differential transform method compared with traditional differential transform method is decreased in s p time, where s is the quantity of accounted discretes, p is the quantity of intervals, over which the given time interval is divided. The multi-step differential transform method gives the principal possibility to get more exact value of random analytic function ) (tx on the end of interval at restricted quantity of discretes of differential spectrum compared with the differential transform method application.
Authors and Affiliations
Viacheslav Gusynin, Andrii Gusynin, Helen Tachinina
Keywords
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- EP ID EP459708
- DOI 10.18372/2306-1472.70.11422
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