Dual approach as empirical reliability for fractional differential equations

P. B. Dubovski, J. A. Slepoi

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations

Abstract

Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the reliable dual approach which fixes this inconsistency. We suggest to use two parallel methods based on the transformation of fractional derivatives through integration by parts or by means of substitution. We introduce the method of substitution and choose the proper discretization scheme that fits the grid points for the by-parts method. The solution is reliable only if both methods produce the same results. As an additional control tool, the Taylor series expansion allows to estimate the approximation errors for fractional derivatives. In order to demonstrate the proposed dual approach, we apply it to linear, quasilinear and semilinear equations and obtain very good precision of the results. The provided examples and counterexamples support the necessity to use the dual approach because either method, used separately, may produce incorrect results. The order of the exactness is close to the exactness of fractional derivatives approximations.

Original languageEnglish
Article number012004
JournalJournal of Physics: Conference Series
Volume2099
Issue number1
DOIs
StatePublished - 13 Dec 2021
EventInternational Conference on Marchuk Scientific Readings 2021, MSR 2021 - Novosibirsk, Virtual, Russian Federation
Duration: 4 Oct 20218 Oct 2021

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