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

By Omid Nikan, Hossein Jafari, Ahmad Golbabai. 2020

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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 H 1 -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.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d61dae8cbb4c3b50e18f87296b471a4d7dee74a1