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

TL;DR

This paper introduces a second-order fast finite difference scheme for the tempered time fractional advection-dispersion equation, effectively handling initial time nonsmoothness with proven stability, convergence, and numerical validation.

Contribution

It presents a novel second-order finite difference scheme specifically designed for tempered time fractional equations with initial singularities, ensuring stability and convergence.

Findings

Scheme achieves second-order accuracy in time and space.

Numerical examples confirm theoretical stability and convergence.

Effective for equations with initial time nonsmoothness.

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.