Open AccessTHE FOURIER-ASYMPTOTIC APPROXIMATION AND ITS APPLICATIONS
Author(s) -
M. Belovs,
Jānis Smotrovs
Publication year - 1998
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1998.9637082
Subject(s) - fourier series , mathematics , generalization , fourier transform , galerkin method , mathematical analysis , spectral method , ordinary differential equation , method of matched asymptotic expansions , asymptotic expansion , asymptotic analysis , boundary (topology) , boundary value problem , differential equation , physics , quantum mechanics , nonlinear system
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.