Geodesic
Method of fast expansions for solving nonlinear differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 13-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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A. D. Chernyshov. Method of fast expansions for solving nonlinear differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 13-24. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_1_a1/

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