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Brzeziński Dariusz W. (Lodz University of Technology, Poland), Ostalczyk Piotr (Lodz University of Technology, Poland)
Accuracy Evaluation of Classical Integer Order Based and Direct Non-integer Order Numerical Algorithms of Non-integer Order Derivatives and Integrals Computations
Annals of Computer Science and Information Systems, 2014, vol. 2, s. 553 - 560, rys., bibliogr. 23 poz.
Algorytmy numeryczne, Rachunek różniczkowy i całkowy, Analiza matematyczna
Numeric algorithms, Calculus, Mathematical analysis
In this paper the authors evaluate in context of numerical calculations accuracy classical integer order and direct non-integer based order numerical algorithms of non-integer orders derivatives and integrals computations. Classical integer order based algorithm involves integer and fractional order differentiation and integration operators concatenation to obtain non-integer order. Riemann-Liouville and Caputo formulas are applied to obtain directly derivatives and integrals of non-integer orders. The following accuracy comparison analysis enables to answer the question, which algorithm of the two is burdened with lower computational error. The accuracy is estimated applying non-integer order derivatives and integrals computational formulas of some elementary functions available in the literature of the subject.(original abstract)
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