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arXiv · 2502.16112

Upwind-and-shifted numerical scheme for fractional convection equation

Lot-Kei Chou·Wan-Na Deng·Yuan-Yuan Huang·Siu-Long Lei
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Abstract

Fundamental solution of a space fractional convection equation of order $\alpha$ is the probability density function of L\'{e}vy flights with long-tailed $\alpha$-stable jump length distribution. By studying an upwind second-order implicit finite difference scheme for the equation with $\alpha\in(0,1)$, an upwind-and-shifted scheme with order $3-\alpha$ is obtained in this paper, and the scheme is shown to be unconditionally stable for a wide range of $\alpha$. Numerical examples, including simulations on a probability density function, are presented showing the effectiveness of the numerical schemes.

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Lot-Kei Chou, Wan-Na Deng, Yuan-Yuan Huang, Siu-Long Lei. 2025-02-22. Upwind-and-shifted numerical scheme for fractional convection equation. https://arxiv.org/abs/2502.16112

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