The Fourier – asymptotic approximation can be obtained for different types of Fourier series by replacing the Fourier coefficients with their asymptotic (n → + 8) approximations beginning with some index n. We obtain some generalization of the classical Galerkin method for the solution of boundary and spectral problems of ordinary differential equations. The numerical examples show that the addition of asymptotic correction allows us to obtain a high accuracy of results.
Belovs, M., & Smotrovs, J. (1998). The Fourier‐asymptotic approximation and its applications. Mathematical Modelling and Analysis, 3(1), 14-24. https://doi.org/10.3846/13926292.1998.9637082
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