Nikan O, Machado J A Tenreiro, Avazzadeh Z, Jafari H
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
Department of Electrical Engineering, ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal.
J Adv Res. 2020 Jun 23;25:205-216. doi: 10.1016/j.jare.2020.06.018. eCollection 2020 Sep.
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.
本文研究在卡普托导数意义下对时间分数阶特里科米型模型进行逼近。该模型常用于描述近声速气体动力学的反常过程。时间半离散化通过有限差分算法计算，而空间离散化则在有限差分模式下使用局部径向基函数获得。局部配置法通过径向基函数展开，利用节点局部集合（称为模板）上函数值的加权和来逼近微分算子。该技术仅考虑配置节点周围每个子域的离散节点。这导致了稀疏系统，并解决了全局配置产生的病态问题。通过离散能量法证明了所提出的时间半离散格式的理论收敛性和稳定性分析。数值结果证实了新方法的准确性和有效性。
