An efficient numerical method for the solution of 2D variable order time fractional mobile–immobile advection–dispersion model

Source abstract

In the literature, there are a few efficient numerical methods with stability and convergence analysis for the solution of variable order fractional partial differential equations in higher dimensions. In this work, we propose an efficient numerical method for the solution of two‐dimensional variable order time fractional mobile–immobile advection–dispersion model with spatially variable convection coefficient. At first, we discretize the time derivatives with a second‐order scheme. Then, we apply the Legendre spectral element method in spatial directions and obtain the fully discrete scheme. We prove that the semi‐discrete scheme is unconditionally stable and present an error estimate for the fully discrete scheme. The numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.