On accurate product integration rules for linear fractional differential equations

This paper addresses the numerical solution of linear fractional differential equations with a forcing term. Competitive and highly accurate Product Integration rules are derived by starting from an equivalent formulation in terms of a Volterra integral equation with a generalized Mittag-Leffler function in the kernel. The error analysis is reported and aspects related to the computational complexity are treated. Numerical tests confirming the theoretical findings are presented. (C) 2010 Elsevier B.V. All rights reserved.