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- W2887016232 abstract "We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters. Subsequently, we develop an efficient strategy to calculate the discrete convolution for the approximation of the fractional operator in the semi-implicit method and we derive an error bound of the fast convolution. The memory requirement and computational cost of the present semi-implicit methods with a fast convolution are about $O(Nlog n_T)$ and $O(Nn_Tlog n_T)$, respectively, where $N$ is a suitable positive integer and $n_T$ is the final number of time steps. Numerical simulations, including the solution of a system of two nonlinear fractional diffusion equations with different fractional orders in two-dimensions, are presented to verify the effectiveness of the semi-implicit methods." @default.
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- W2887016232 date "2018-08-06" @default.
- W2887016232 modified "2023-10-18" @default.
- W2887016232 title "A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations" @default.
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- W2887016232 doi "https://doi.org/10.48550/arxiv.1808.02170" @default.
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