Numerical analysis of the fractional evolution model for heat flow in materials with memory

This paper develops the solution of the two-dimensional time fractional evolution model using finite difference scheme derived from radial basis function (RBF-FD) method. In this dis-cretization process, a finite difference formula is implemented to discrete the temporal variable, while the local RBF-FD formulation is utilized to approximate the spatial variable. The pattern of data distribution in the local support domain is assumed as having a fixed number of nodes. The local RBF-FD is based on the local support domain that leads to a sparsity system and also avoids the ill-conditioning problem caused by global collocation method. The stability and conver-gence of time-discrete approach in H-1-norm are discussed by means of the energy method. Numer-ical results illustrate the proposed method and demonstrate that it provides accurate solutions on regular and irregular computational domains. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).