The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition

In this paper, we consider the numerical solution of the time-fractional diffusion equation with a non-local boundary condition. The method of approximate particular solutions (MAPS) using multiquadric radial basis function (MQ-RBF) is employed for this equation. Due to the accuracy of the MQ-based meshless methods is severely influenced by the shape parameter, we adopt a leave-one-out cross validation (LOOCV) algorithm proposed by Rippa [34] to enhance the performance of the MAPS. The numerical results obtained show that the proposed numerical algorithm is accurate and computationally efficient for solving time-fractional diffusion equation with a non-local boundary condition. (C) 2015 Elsevier Ltd. All rights reserved.