Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 100, Issue 1, Pages 20-46Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2022.2078663
Keywords
Fractional second linear multistep methods; linear stability; Caputo fractional derivative; consistency
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This paper introduces the explicit forms of the fractional second linear multistep methods for solving fractional differential equations. The properties and characteristics of these methods are analyzed and verified through experiments.
In this paper, the explicit forms of the fractional second linear multistep methods (FSLMMs) are introduced for solving fractional differential equations (FDEs) of the fractional-order in (1, 2). These explicit FSLMMs are constructed based on fractional backward difference formulas 1, 2, and 3 (FBDF1, FBDF2, and FBDF3) with the first, second, third, and fourth orders of convergence. Also, the monotonicity of these FBDFs is considered when the order of fractional derivatives lies into (1, 2). The order of consistency, linear stability, and the order of convergence of these explicit methods are analysed. Moreover, the stability regions of the proposed methods are completely studied in the stability topic. Finally, four experimental examples are presented to confirm the proposed theories.
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