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

Abstract

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 discretization 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 convergence of time-discrete approach in H1-norm are discussed by means of the energy method. Numerical results illustrate the proposed method and demonstrate that it provides accurate solutions on regular and irregular computational domains.