Numerical calculation of non-autonomous dynamic models with nonlinearities in the form of non-power elemental functions
The numerical calculation method of dynamic models with nonlinearities described by elementary non-power functions is represented. The computational difficulties in applying power series are analyzed. To overcome computational difficulties, a constructive procedure based on the analytical-numerical method of analysis developed by the authors is proposed. The numerical procedure is applicable to the models described by a system of nonlinear differential equations in the normal form of Cauchy. The proposed procedure, while preserving all the advantages of the power-series apparatus, eliminates the necessity for constructing the power-series compositions and special estimates, as well as raises the formalization of dynamic model calculations with non-power nonlineari-ties. The proposed numerical procedure uses the evaluations of the desired solutions and manages the boundaries of one-dimensional domains of exact solutions in order to bring them to unknown exact solutions. The advantages of the procedure are highlighted during the calculation of nonlinear autonomous dynamic model of the type «damped pendulum».
Authors: Yu. A. Bychkov, E. B. Solovyeva, S. V. Scherbakov
Direction: Electrical Engineering
Keywords: nonlinear dynamic system, mathematical model, nonlinear differential equation, analytical-numerical method
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