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A numerical method for the distributed order time-fractional diffusion equation

Ford, N.J.; Morgado, M. Luísa; Rebelo, Magda

Proceedings of the IEEE International Conference on Fractional Differentiation and Its Applications'14, (2014), 1-6

This paper is devoted to the numerical approximation of the diffusion equation with distributed order in time. A numerical method is proposed in the case where the order of the time derivative is distributed over the interval [0, 1], and results concerning the stability and convergence of that scheme are provided. Two numerical examples are presented illustrating the theoretical numerical results.