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

• Autorzy: Brzeziński D. W. , Ostalczyk P.

Identyfikatory

DOI

10.2478/bpasts-2014-0078

• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

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

PL

dokładność obliczeń numerycznych; kwadratury Gaussa- Jacobiego z przyjętą funkcją wagi; arbitralna precyzja; całkowanie numeryczne; równanie Abela

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2014
• Tom: Vol. 62, nr 4
• Strony: 723--733
• Opis fizyczny: Bibliogr. 24, tab., wykr.

Twórcy

autor

Brzeziński D. W.

• Faculty of Electrical, Electronic, Computer and Control Engineering, Institute Of Applied Computer Science, Lodz University of Technology, 18/22 Stefanowskiego St., 90-537 Łódź, Poland

autor

Ostalczyk P.

• Faculty of Electrical, Electronic, Computer and Control Engineering, Institute Of Applied Computer Science, Lodz University of Technology, 18/22 Stefanowskiego St., 90-537 Łódź, Poland

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