A family of Adams exponential integrators for fractional linear systems

摘要

The numerical solution of linear time–invariant systems of fractional order is investigated. The approach proposed in the paper generates a family of exponential integrators related to Adams methods for ordinary di erential equations. The weights of the resulting convolution quadratures are based on some generalized Mittag–Leffler functions with matrix arguments; the problem of their efficient evaluation by means of a technique combining the numerical inversion of the Laplace transform and the rational approximation of the exponential is treated in detail. Some aspects related to problems of large size are also discussed. Numerical experiments are provided to show the accuracy and effectiveness of the proposed approach.