Volume 44, pp. 289-305, 2015.

An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

N. J. Ford, M. L. Morgado, and M. Rebelo

Abstract

In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval $(0,1)$. An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.

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Key words

Caputo derivative, fractional differential equation, subdiffusion, finite difference method, distributed order differential equation

AMS subject classifications

35R11, 65M06, 65M12