Stability analysis of difference-Legendre spectral method for two-dimensional Riesz space distributed-order diffusion-wave model

Abstract

In this manuscript, a numerical method with high accuracy and efficiency based on the difference-Legendre spectral method is proposed for obtaining the numerical solutions of the two-dimensional space-time distributed-order fractional diffusion-wave equations with the Riesz space fractional derivative. The difference method by an approximate formula respect to the time variable is used to discrete the distribution-order integral part consisting of Caputo fractional derivative. Also, the Gauss quadrature formula respect to the space variable is used to estimate the distribution-order integral part consisting of Riesz space derivative. Further, the stability and convergence analyses are studied for the numerical estimation. Some numerical examples are displayed to show the effectiveness of proposed methods.