POLISH ACADEMY of SCIENCES
TECHNICAL SCIENCES
| BULLETIN
of the
POLISH ACADEMY of SCIENCES TECHNICAL SCIENCES |
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| Volume
60, Issue 2, June 2012
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| Aims&Scope, Subscription | Editors | Authors' guide | to read PDF files | mirror: http://fluid.ippt.gov.pl/~bulletin/ |
| pp 285 - 292 |
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Numerical evaluation of fractional differ-integrals of some periodical functions via the IMT transformation |
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| D. BRZEZINSKI and P. OSTALCZYK |
| This paper presents accuracy evaluation of the numerical calculations of the fractional differ-integrals. We focus on applying the Riemann-Liouville formula, on singularity, which appears while using classical form of this formula. To calculate it we use the Newton-Cotes' Quadrature and additionally two Gaussian rules. Using this different approach to the IMT Transformation, transforming the "core" integrand of Riemann-Liouville formula, we point the possible way of increasing the accuracy of the calculations. We use our own tools and compare obtained results with, where possible, exact values, where not - values obtained using an excellent method of integration incorporated in Mathematica. |
| Key words: |
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fractional-order derivatives and integrals, accuracy of numerical calculations, numerical integration, IMT Transformation, periodical functions |
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| Copyright ® Bulletin of the Polish Academy of Sciences: Technical Sciences |
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