Abstract In this paper, a discrete orthogonal spline collocation method combining with a second-order Crank-Nicolson weighted and shifted Grünwald integral (WSGI) operator is proposed for solving time-fractional wave equations based on its equivalent partial integro-differential equations. The stability and convergence of the schemes have been strictly proved. Several numerical examples in one variable and in two space variables are given to demonstrate the theoretical analysis.

中文翻译：

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二维时间分数扩散波方程结合WSGI差分格式的Crank-Nicolson正交样条搭配法

摘要 本文提出了一种结合二阶Crank-Nicolson加权移位Grünwald积分(WSGI)算子的离散正交样条搭配方法，基于其等效偏积分微分方程求解时间分数波动方程。方案的稳定性和收敛性得到了严格证明。给出了一个变量和两个空间变量的几个数值例子来证明理论分析。