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A family of Adams exponential integrators for fractional linear systems

机译：分数线性系统的Adams指数积分器族

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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 diu000berential 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.
机译：研究了分数阶线性时不变系统的数值解。本文提出的方法生成了与普通二阶微分方程的Adams方法有关的指数积分族。卷积正交的权​​重是基于一些带有矩阵自变量的广义Mittag-Leffler函数。详细讨论了通过结合拉普拉斯变换的数值反演和指数的有理逼近的技术对其进行有效评估的问题。还讨论了与大尺寸问题有关的某些方面。数值实验表明了该方法的准确性和有效性。

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