Abstract
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 . 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 , 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
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