Numerical analysis for distributed-order differential equations

In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form integral(m)(0) A(r. D(*)(r)u(t))dr = f(t) where in is a positive real number and where the derivative D-*(r) taken to be a fractional derivative of Caputo type of order r. We give a convergence theory for our method and conclude with some numerical examples. (C) 2008 Elsevier B.V. All rights reserved.