This article is devoted to obtain the numerical solution for a class of nonlinear two-dimensional distributed-order time fractional diffusion equations. We discretize the problem by using a finite difference scheme in the time direction. Then, we solve the discretized nonlinear problem by a collocation approach based on the Legendre polynomials. The numerical algorithm is fully described and convergence analysis of the scheme is evaluated. Finally, few numerical implementations are presented to highlight the flexibility and the convergence rate of this method.
