A stable numerical investigation based on geometric greedy points for 2D time-fractional partial integro-differential equations with singular kernels

Abstract

This paper develops a stable numerical method based on RBFs to solve two-dimensional time-fractional partial integro-differential equations with singular kernels. The spatial discretization uses an RBF-generated Hermite finite difference approach, which applies a geometric greedy sparse approximation technique for node selection, ensuring accuracy and controlling consistency errors. The temporal direction is discretized using a nonuniform formulation to achieve faster and more accurate temporal convergence compared to the uniform formulation. The method includes a detailed analysis of convergence and stability. Its accuracy and efficiency are tested with numerical examples, including cases with nonsmooth initial conditions, and compared to other existing methods, showing its superior performance.