Some high-order difference schemes for the distributed-order differential equations

Two difference schemes are derived for both one-dimensional and two-dimensional distributed-order differential equations. It is proved that the schemes are unconditionally stable and convergent in an L-1(L-infinity) norm with the convergence orders O(tau(2)+ h(2)+ Delta alpha(2)) and O(tau(2)+ h(4)+ Delta alpha(4)) , respectively, where tau, h and Delta alpha are the step sizes in time, space and distributed-order variables. Several numerical examples are given to confirm the theoretical results. (C) 2015 Elsevier Inc. All rights reserved.