A comparison study of solving diffusion equations with different algorithm methods

A comparison study for solving diffusion equations with different algorithm methods is studied to understand the oxygen vacancy defect transport under the electric field. We compare computational efficiency and numerical accuracy with different algorithm methods, including finite difference, finite element (COMSOL), and Fourier-Chebysev spectral methods. All the results of oxygen vacancy distribution under an electric field from different algorithm methods are compared with the analytical solution results. Two kinds of boundary conditions are used in solving diffusion equations and the absolute error of different methods are discussed. The main purpose of these results is to provide guidance for studying the role of point defect transport in the degradation and breakdown of devices