On the choice of approximating functions
Abstract
The accuracy of the solutions obtained by any of the known approximate methods depends on how well the functions approximating this solution are chosen. It is natural to expect that, while maintaining the desired solution in the expansion series, even the minimum number of terms of the series (and it is this case that is of the greatest interest for practical calculations), the approximate solution will differ insignificantly from the exact one if the approximating functions satisfy all boundary conditions...
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References
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- Papkovich P. F. On the choice of fundamental functions in the Rayleigh-Ritz method. In the book. "Works on the strength of the ship." Sudpromgiz, 1956. Duncan W. I. Вг. ARC, R. and М., 1947.
- Wіllіams D. Вг. ARC, R. and М., 1937.