科研之友
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摘要
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 (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(4+h 4), where and h are the temporal and spatial stepsizes, respectively. Finally, several numerical examples are presented to verify the theoretical results.
