In this paper, a generalized finite difference method (GFDM) is proposed and analyzed for meshless numerical solution of the time-fractional diffusion-wave equation. Two -order accurate temporal discretization schemes are presented by using the L1 formula and the original H2N2 or fast H2N2 formulas to discretize the time-fractional derivative of order . The stability of the temporal discretization schemes is analyzed. Then, the time-fractional diffusion-wave initial-boundary value problem is transformed into a series of time-independent integer-order boundary value problems, and discrete linear algebraic systems are built by the application of the GFDM. Accuracy analysis of the GFDM with both original H2N2 and fast H2N2 formulas is presented in theory, and numerical experimental results are provided to verify the theoretical results and the effectiveness of the proposed meshless method.

中文翻译：

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时间分数阶扩散波方程的无网格广义有限差分法分析


本文提出并分析了一种广义有限差分法（GFDM），用于时间分数扩散波方程的无网格数值求解。利用L1公式和原始H2N2或快速H2N2公式对阶次时间分数阶导数进行离散化，提出了二阶精确时间离散化方案。分析了时间离散化方案的稳定性。然后，将时间分数扩散波初边值问题转化为一系列与时间无关的整数阶边值问题，并应用GFDM建立离散线性代数系统。从理论上对原始 H2N2 和快速 H2N2 公式的 GFDM 进行了精度分析，并提供了数值实验结果来验证理论结果和所提出的无网格方法的有效性。