THE POSSIBILITY OF APPLYING THE POLYNOMIAL APPROXIMATION METHOD TO THE SOLUTION OF PROBLEMS IN THE RESEARCH OF PERIODIC NON-SINUSOIDAL FUNCTIONS

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THE POSSIBILITY OF APPLYING THE POLYNOMIAL APPROXIMATION METHOD TO THE SOLUTION OF PROBLEMS IN THE RESEARCH OF PERIODIC NON-SINUSOIDAL FUNCTIONS

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This paper presents an electrical circuit connected to a non-sinusoidal power source. In real consumers of electrical energy, due to the presence of parametric elements, the shape of the voltage and current curves distort the shapes of these function curves at the receivers, resulting in additional energy losses and a reduction in their efficiency. Graphical, graph-analytical and analytical methods are used to calculate such schemes. A polynomial approximation method for numerical integration of the function is applied as an analytical solution, since any continuous function can be approximated with any precision within any closed interval by a polynomial of sufficiently high degree. We describe the classical Wee strass theorem for approximation. Graphical representations of the geometrical interpretation of the multistep method and a general view of the multistep formula for numerical integration of order "k" are shown. The term numerical integration is introduced because methods of this type are similar to those used for numerical integration of functions. The order of a numerical integration method refers to the maximum degree of polynomial solution in which the formula gives the exact value for x(t n+i) in the absence of rounding error.

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# Non-sinusoidal function# analytical calculation# continuous function# function approximation# second-degree polynomial# Taylor method

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https://eroi.uz/11.0008/A0922-0066

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