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• W4313461444 abstract "We propose high-order schemes for nonlinear fractional initial value problems. We split the fractional integral into a history term and a local term. We take advantage of the sum of exponentials (SOE) scheme in order to approximate the history term. We also use a low-order quadrature scheme to approximate the fractional integral appearing in the local term and then apply a spectral deferred correction (SDC) method for the approximation of the local term. The resulting one-step time-stepping methods have high orders of convergence, which make adaptive implementation and accuracy control relatively simple. We prove the convergence and stability of the proposed schemes. Finally, we provide numerical examples to demonstrate the high-order convergence and adaptive implementation." @default.
• W4313461444 created "2023-01-06" @default.
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• W4313461444 date "2022-12-19" @default.
• W4313461444 modified "2023-09-30" @default.
• W4313461444 title "High-Order Schemes for Nonlinear Fractional Differential Equations" @default.
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• W4313461444 doi "https://doi.org/10.3390/fractalfract6120748" @default.
• W4313461444 hasPublicationYear "2022" @default.
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