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High‐order algorithms for Riesz derivative and their applications (V)
Author(s) -
Ding Hengfei,
Li Changpin
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22169
Subject(s) - mathematics , combing , riesz potential , order (exchange) , operator (biology) , fractional calculus , partial derivative , differential operator , m. riesz extension theorem , derivative (finance) , algorithm , scheme (mathematics) , riesz transform , mathematical analysis , biochemistry , chemistry , cartography , finance , repressor , transcription factor , financial economics , economics , gene , geography
In this article, based on the idea of combing symmetrical fractional centred difference operator with compact technique, a series of even‐order numerical differential formulas (named the fractional‐compact formulas) are established for the Riesz derivatives with order α ∈ ( 1 , 2 ) . Properties of coefficients in the derived formulas are studied in details. Then applying the constructed fourth‐order formula, a difference scheme is proposed to solve the Riesz spatial telegraph equation. By the energy method, the constructed numerical algorithm is proved to be stable and convergent with order O ( τ 4 + h 4 ) , where τ and h are the temporal and spatial stepsizes, respectively. Finally, several numerical examples are presented to verify the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1754–1794, 2017