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- W2948345770 abstract "In this article, we introduce two families of novel fractional $theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $mathit{I}^{alpha}$ with a second order convergence rate. A new fractional BT-$theta$ method connects the fractional BDF2 (when $theta=0$) with fractional trapezoidal rule (when $theta=1/2$), and another novel fractional BN-$theta$ method joins the fractional BDF2 (when $theta=0$) with the second order fractional Newton-Gregory formula (when $theta=1/2$). To deal with the initial singularity, correction terms are added to achieve an optimal convergence order. In addition, stability regions of different $theta$-methods when applied to the Abel equations of the second kind are depicted, which demonstrate the fact that the fractional $theta$-methods are A($vartheta$)-stable. Finally, numerical experiments are implemented to verify our theoretical result on the convergence analysis." @default.
- W2948345770 created "2019-06-14" @default.
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- W2948345770 date "2019-06-04" @default.
- W2948345770 modified "2023-09-26" @default.
- W2948345770 title "Two families of novel second-order fractional numerical formulas and their applications to fractional differential equations" @default.
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- W2948345770 doi "https://doi.org/10.48550/arxiv.1906.01242" @default.
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