Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas
Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas
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DOI：
10.21042/amns.2016.1.00003
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发表时间：
2016
影响因子：
3.1
通讯作者：
D. Brzezinski
中科院分区：
文献类型：
--
作者：
D. Brzezinski
本文给出了Riemann-Liouville/Caputo公式应用中提高分数阶导数精度和积分计算的三种方法，并对其有效性进行了评价。它们的思想要么是将公式中的难被积量转化为应用数值积分方法的高精度计算要求，要么是采用数值积分方法对被积量中的难特征进行高精度处理。通过将增加的精度纳入计算，获得了额外的精度增益。采用本文提出的方法实际提高了精度，并与现有的多种集成方法进行了比较。
Abstract 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.