Spline-Fourier Approximations of Discontinuous Waves
Дата
Авторы
Anguelov,Roumen
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
In the Fourier series approximation of real functions discontinuities of the functions or their derivatives cause problems like Gibbs phenomenon or slow uniform convergence. In the case of a finite number of isolated discontinuities the problems can be to a large extend rectified by using periodic splines in the series. This modified Fourier series (Spline-Fourier series) is applied to the numerical solution of the wave equation (in periodic form) where discontinuities in the data functions or their derivatives appear quite often. The solution is sought in the form of a Spline-Fourier series about the space variable and close bounds are obtained using a certain iterative procedure of Newton type.
Ключевые слова
Validated numerics , Fourier hyper functoid , Wave equation