METHODS OF MODERNIZING THE APPEAL OF LAPLACE TRANSFORMATION IN THE PYTHON LANGUAGE TO SOLVE ELECTRICAL CIRCUITS

In applied mathematics, the Laplace transform is very relevant. Thus, in mathematics, mechanics and engineering, the operational method based on the Laplace transform is widely and very successfully used to solve entire class ofproblems. The object of the study is the integral from the Riemann-Mellin formula for inverting the Laplace transform and approximating it with the help of Fourier series of a numerical aggregate. In this paper we study the method of inversion of the Laplace transform by expanding the original function into a Fourier series with respect to the sines of odd multiple arcs. Also an analogous method based on the expansion of the function in the Fourier series of Legendre polynomials is developed, during which examples were considered that helped to carry out a comparative analysis of the convergence rates of canonical and developed methods. A numerical apparatus was developed and implemented in the programming language Python, which clearly demonstrates the predicted hypotheses.

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