A New Fast Finite Difference Scheme for Tempered Time Fractional Advection-Dispersion Equation with a Weak Singularity at Initial Time

2025/12/17 by Huang, Liangcai, Lü, Shujuan
#26A33 and 35R11 and 65M12 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2512.15141

Abstract

In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we investigate the uniqueness, stability, and convergence of the scheme. Furthermore, we prove that the scheme achieves second-order convergence in both time and space. Finally, corresponding numerical examples are provided.

Citations

• Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
• A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model
• Analytical and numerical investigation on the tempered time-fractional operator with application to the Bloch equation and the two-layered problem
• Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels
• A tempered subdiffusive Black-Scholes model

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• Numerical method based on Galerkin approximation for the fractional\n advection-dispersion equation