Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models

A numerical scheme based on Haar wavelets coupled with finite differences is suggested to study variable order time fractional partial differential equations (TFPDEs). The technique is tested on (1 + 1)-dimensional advection dispersion and (1 + 2)-dimensional advection diffusion equations. In the proposed scheme, time fractional derivative is firstly approximated by quadrature formula, and then finite differences are combined with one and two dimensional Haar wavelets. With the help of suggested method the TFPDEs convert to a system of algebraic equations which is easily solvable. Also convergence of the proposed scheme has been discussed which is an important part of the present work. For validation, the obtained results are matched with earlier work and exact solutions. Computations illustrate that the proposed scheme has better outcomes. (C) 2019 Elsevier Inc. All rights reserved.