High-accuracy numerical integration methods for fractional order derivatives and integrals computations

Brak miniatury

Data

2014

Tytuł czasopisma

ISSN czasopisma

Tytuł tomu

Wydawca

Abstrakt

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).

Opis

Słowa kluczowe

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

Cytowanie

Bulletin of the Polish Academy of Sciences Technical Sciences, Vol. 62, Issue 4, 2014, Pages 723–733