Abstract
A method is proposed for constructing fast converging Fourier series with the help of a special boundary function M q . The convergence rate of the series is determined by the order q of M q , which makes it possible to use a small number of series terms. The general theory of constructing fast expansions is described, the error of the partial sum of a series is estimated, and an example of a non- linear integrodifferential problem is considered. Due to its remarkable properties, the fast expansion method can be effectively used in applications.
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Original Russian Text © A.D. Chernyshov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 1, pp. 13–24.
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Chernyshov, A.D. Method of fast expansions for solving nonlinear differential equations. Comput. Math. and Math. Phys. 54, 11–21 (2014). https://doi.org/10.1134/S0965542514010060
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DOI: https://doi.org/10.1134/S0965542514010060