2025/02/22 by Lot‐Kei Chou, Chou, Lot-Kei, Yuanyuan Huang +4
Mathematics · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2502.16112
Fundamental solution of a space fractional convection equation of order α is the probability density function of Lévy flights with long-tailed α-stable jump length distribution. By studying an upwind second-order implicit finite difference scheme for the equation with α∈(0,1), an upwind-and-shifted scheme with order 3-α is obtained in this paper, and the scheme is shown to be unconditionally stable for a wide range of α. Numerical examples, including simulations on a probability density function, are presented showing the effectiveness of the numerical schemes.