An RBF-based method with optimal point selection for solving two-dimensional multi-term time-fractional PIDEs with weakly singular kernels

This paper presents a novel numerical method using radial basis functions (RBFs) to solve two-dimensional multi-term time-fractional partial integro-differential equations with multi-term weakly singular kernels. The spatial discretization is based on an RBF-generated finite difference method, combined with geometrically optimal point selection for efficient stencil design. The key contribution of this study is the development of a greedy algorithm that constructs quasi-uniform point sets by balancing the fill distance and separation distance, thereby ensuring asymptotically optimal domain coverage. By generating weights with desirable properties, the method significantly enhances stability. A series of numerical experiments has been conducted to evaluate the efficiency and accuracy of the proposed method. The results, presented through detailed tables and figures, confirm the method’s effectiveness in accurately solving the target equations. Furthermore, performance evaluations using various examples highlight the method’s superiority and reliability.