This paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via a finite difference algorithm, while the spatial discretization is obtained using the local radial basis function in a finite difference mode. The local collocation method approximates the differential operators using a weighted sum of the function values over a local collection of nodes (named stencil) through a radial basis function expansion. This technique considers merely the discretization nodes of each subdomain around the collocation node. This leads to sparse systems and tackles the ill-conditioning produced of global collocation. The theoretical convergence and stability analyses of the proposed time semi-discrete scheme are proved by means of the discrete energy method. Numerical results confirm the accuracy and efficiency of the new approach.

本文从Caputo导数的角度处理时间分数Tricomi型模型的近似问题。该模型通常用于描述近音速气体动力学的异常过程。时间半离散化是通过有限差分算法计算的，而空间离散化是使用局部径向基函数以有限差分模式获得的。局部配置方法通过径向基函数扩展在节点的本地集合（称为模具）上使用函数值的加权和来近似微分算子。该技术仅考虑并置节点周围的每个子域的离散化节点。这导致系统稀疏，并解决了因全球配置而导致的不良情况。通过离散能量方法证明了所提出的时间半离散方案的理论收敛性和稳定性。数值结果证实了该新方法的准确性和效率。