Application of alternative Legendre polynomials for solving a class of
two-dimensional nonlinear time-fractional diffusion equations of
distributed-order
- AFSHIN BABAEI,
- Sahar Banihashemi
Abstract
This paper is devoted to finding the numerical solution for a class of
nonlinear two-dimensional distributed-order time-fractional diffusion
equation. A finite difference scheme is used to discretize the problem
in the time direction. Then, a collocation approach based on the
alternative Legendre polynomials is employed to solve the discretized
nonlinear problem. The numerical algorithm is fully described and
convergence analysis of the method is evaluated. Finally, some numerical
implementations are provided to highlight the convergence rate and the
flexibility of this approach.