Numerical Evaluation of Fractional Differ-Integral of Some Elementary Functions via Inverse Transformation

• Autorzy: Ostalczyk P. , Brzeziński D.
• Języki publikacji: EN

Abstrakty

EN

This paper presents methods of calculating fractional differ-integrals numerically. We discuss extensively the pros and cons of applying the Riemann-Liouville formula, as well as direct approach in form of The Grünwald-Letnikov method. We take closer look at the singularity, which appears when using classical form of Riemann-Liouville formula. To calculate Riemann-Liouville differ-integral we use very well-known techniques like The Newton-Cotes Midpoint Rule. We also use two Gauss formulas. By implementing transformation of the core integrand of Riemann-Liouville formula (we called it “the inverse transformation”), we would like to point the possible way of reducing errors when calculating it. The core of this paper is the subject of reducing the absolute error when calculating Riemann-Liouville differ-integrals of some elementary functions; we use our own C++ programs to calculate them and compare obtained results of all methods with, where possible, exact values, where not – with values obtained using excellent method of integration incorporated in Mathematica. We will not discuss complexity of numerical calculations. We will focus solely on minimization of the absolute errors.

Słowa kluczowe

EN

Riemann-Liouville formula; inverse transformation

PL

formuła Riemanna-Liouvilla; transformacja

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2011
• Tom: Vol. 5, no. 2
• Strony: 86--95
• Opis fizyczny: Bibliogr. 31 poz., Wykr.

Twórcy

autor

Ostalczyk P.

autor

Brzeziński D.

• Technical University of Lodz, Łódź,

Bibliografia

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