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• W2896711392 abstract "According to the principle of conservation of mass and the fractional Fick’s law, a new two-sided space-fractional diffusion equation was obtained. In this paper, we present two accurate and efficient numerical methods to solve this equation. First we discuss the alternating-direction finite difference method with an implicit Euler method (ADI–implicit Euler method) to obtain an unconditionally stable first-order accurate finite difference method. Second, the other numerical method combines the ADI with a Crank–Nicolson method (ADI–CN method) and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. Finally, numerical solutions of two examples demonstrate the effectiveness of the theoretical analysis." @default.
• W2896711392 created "2018-10-26" @default.
• W2896711392 creator A5019496564 @default.
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• W2896711392 date "2018-10-23" @default.
• W2896711392 modified "2023-09-24" @default.
• W2896711392 title "Alternating-direction implicit finite difference methods for a new two-dimensional two-sided space-fractional diffusion equation" @default.
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• W2896711392 doi "https://doi.org/10.1186/s13662-018-1836-z" @default.
• W2896711392 hasPublicationYear "2018" @default.
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