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• W2893600178 abstract "In this paper, we first construct an efficient scheme for nonlinear Caputo fractional differential equations with the initial value and the fractional degree [Formula: see text]. Then, the unconditional stability and the superlinear convergence with the order [Formula: see text] of the proposed scheme are strictly proved and discussed. Due to the nonlocal property of fractional operators, the new scheme is time-consuming for long-time simulations. Thus, a fast implement of the proposed scheme is presented based on the sum-of-exponentials (SOE) approximation for the kernel [Formula: see text] on the interval [Formula: see text] in the Riemann–Liouville integral, where [Formula: see text] is the stepsize. Some numerical experiments are provided to support the theoretical results of the new scheme and demonstrate the computational performance of its fast implement." @default.
• W2893600178 created "2018-10-05" @default.
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• W2893600178 date "2019-02-01" @default.
• W2893600178 modified "2023-09-23" @default.
• W2893600178 title "A superlinear convergence scheme for nonlinear fractional differential equations and its fast implement" @default.
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• W2893600178 doi "https://doi.org/10.1142/s1793962319410010" @default.
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