Accuracy evaluation of classical integer order and direct non-integer order based numerical algorithms of non-integer order derivatives and integrals computations

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...

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Bibliographic Details
Published in2014 Federated Conference on Computer Science and Information Systems pp. 553 - 560
Main Authors Brzezinski, Dariusz W., Ostalczyk, Piotr
Format Conference Proceeding
LanguageEnglish
Published Polish Information Processing Society 01.09.2014
Subjects
Accuracy
Algorithm design and analysis
Complexity theory
Computer science
Context
Educational institutions
Estimation
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DOI10.15439/2014F190

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Summary: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.
DOI:10.15439/2014F190