ESTIMATE OF ACCURACY OF APPROXIMATE SOLUTIONS OF NON-LINEAR BOUNDARY VALUE PROBLEMS BY THE MULTI-STEP DIFFERENTIAL TRANSFORM METHOD
Keywords:approximate solution, differential transform method, estimate of accuracy, multi-step differential transform method, simulation, upper and lower bounds of error estimate
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 time, where is the quantity of accounted discretes, 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 on the end of interval at restricted quantity of discretes of differential spectrum compared with the differential transform method application.
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