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- W3013709683 abstract "We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order $3-nu$ can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results." @default.
- W3013709683 created "2020-04-03" @default.
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- W3013709683 date "2020-02-22" @default.
- W3013709683 modified "2023-09-26" @default.
- W3013709683 title "Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy" @default.
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- W3013709683 doi "https://doi.org/10.48550/arxiv.2002.09733" @default.
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