- Tytuł:
- High-accuracy numerical integration methods for fractional order derivatives and integrals computations
- Autorzy:
-
Brzeziński, D. W.
Ostalczyk, P. - Powiązania:
- https://bibliotekanauki.pl/articles/202213.pdf
- Data publikacji:
- 2014
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
accuracy of numerical calculations
fractional-order derivatives and integrals
double exponential formula
gauss-jacobi quadrature with adopted weight function
arbitrary precision
numerical integration
abel’s integral equation
dokładność obliczeń numerycznych
kwadratury Gaussa- Jacobiego z przyjętą funkcją wagi
arbitralna precyzja
całkowanie numeryczne
równanie Abela - Opis:
- In this paper the authors present highly accurate and remarkably efficient computational methods for fractional order derivatives and integrals applying Riemann-Liouville and Caputo formulae: the Gauss-Jacobi Quadrature with adopted weight function, the Double Exponential Formula, applying two arbitrary precision and exact rounding mathematical libraries (GNU GMP and GNU MPFR). Example fractional order derivatives and integrals of some elementary functions are calculated. Resulting accuracy is compared with accuracy achieved by applying widely known methods of numerical integration. Finally, presented methods are applied to solve Abel’s Integral equation (in Appendix).
- Źródło:
-
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 723-733
0239-7528 - Pojawia się w:
- Bulletin of the Polish Academy of Sciences. Technical Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł