A second-order accurate numerical method for the space-time tempered fractional diffusion-wave equation

TL;DR

This paper develops a high-order, unconditionally stable numerical method for solving the space-time tempered fractional diffusion-wave equation, with proven accuracy and verified through numerical experiments.

Contribution

It introduces a second-order accurate numerical scheme for the space-time tempered fractional diffusion-wave equation, with theoretical stability and error analysis.

Findings

Schemes are unconditionally stable.

Global truncation error is D7( au^2+h^2).

Numerical verification confirms theoretical results.

Abstract

This paper focuses on providing the high order algorithms for the space-time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being theoretically proved and numerically verified.