Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas
In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the for...
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| Format: | Article |
| Language: | English |
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Sciendo
2016-01-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
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| Online Access: | https://doi.org/10.21042/AMNS.2016.1.00003 |
| _version_ | 1818744624430186496 |
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| author | Brzeziński Dariusz W. |
| author_facet | Brzeziński Dariusz W. |
| author_sort | Brzeziński Dariusz W. |
| collection | DOAJ |
| description | In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration. |
| first_indexed | 2024-12-18T02:47:16Z |
| format | Article |
| id | doaj.art-6175b8ea14724c7ba8748522e7933ed4 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-18T02:47:16Z |
| publishDate | 2016-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-6175b8ea14724c7ba8748522e7933ed42022-12-21T21:23:32ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562016-01-0111234410.21042/AMNS.2016.1.00003Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo FormulasBrzeziński Dariusz W.0Institute of Applied Computer Science, Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology, 18/22Stefanowskiego St., 90-924 Łódź, PolandIn the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.https://doi.org/10.21042/AMNS.2016.1.00003numerical integrationfractional order derivatives and integrals65-0465k0541-0441a55 |
| spellingShingle | Brzeziński Dariusz W. Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas Applied Mathematics and Nonlinear Sciences numerical integration fractional order derivatives and integrals 65-04 65k05 41-04 41a55 |
| title | Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas |
| title_full | Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas |
| title_fullStr | Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas |
| title_full_unstemmed | Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas |
| title_short | Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas |
| title_sort | accuracy problems of numerical calculation of fractional order derivatives and integrals applying the riemann liouville caputo formulas |
| topic | numerical integration fractional order derivatives and integrals 65-04 65k05 41-04 41a55 |
| url | https://doi.org/10.21042/AMNS.2016.1.00003 |
| work_keys_str_mv | AT brzezinskidariuszw accuracyproblemsofnumericalcalculationoffractionalorderderivativesandintegralsapplyingtheriemannliouvillecaputoformulas |