Numerical approximation of fourth-order fractional diffusion-wave systems using finite difference and discontinuous Galerkin method

This study develops a finite difference/local discontinuous Galerkin (LDG) framework for solving a fourth-order fractional diffusion-wave equation. The temporal fractional operator is approximated through a finite difference approach, achieving a truncation accuracy of $O((\mathrm{\Delta }t{)}^{3-\alpha })$, where $\mathrm{\Delta }t$ denotes the time increment and $\alpha$ represents the fractional order. For spatial discretization, LDG technique is employed, which leads to a fully implicit discrete formulation of the considered model. By applying mathematical induction, we establish the unconditional stability and convergence of the proposed algorithm. A series of computational experiments is presented to verify the theoretical error bounds.