A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation
This work provides an efficient numerical scheme for solving a class of nonlinear fractional wave equations, which is important for computational scientists working on fractional PDEs.
The authors developed a fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation, achieving second-order unconditional convergence in the discrete H1-norm. Numerical examples confirm the method's efficiency.
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the recently established fast L2-1σ formula and a weighted approach. Then we apply the discretization to construct a fully fast linearized discrete scheme for the nonlinear problem under consideration. The nonlinear term, which just fulfills the Lipschitz condition, will be evaluated on the previous time level. Therefore only linear systems are needed to be solved for obtaining numerical solutions. The proposed scheme is shown to have second-order unconditional convergence with respect to the discrete H1-norm. Numerical examples are provided to justify the efficiency.