论文标题
分数导数及其应用的新扩散表示
A New Diffusive Representation for Fractional Derivatives and its Application
论文作者
论文摘要
事实证明，分数衍生物的扩散表示是在构建快速和内存有效的数值方法的有用工具，用于求解分数微分方程。在这种方法的许多已知变体中，一个普遍的挑战是，它们需要某些积分的数值近似在一个无限的积分上，该积分的积分相当缓慢地衰减，这意味着它们的数值处理是困难而昂贵的。我们提出了这种扩散表示的新颖变体。该形式还需要在无界域上积分不可分割的数值近似，但是集成剂的衰减速度要快得多。这允许使用具有更好收敛属性的良好建立的正交规则。
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known variants of this approach is that they require the numerical approximation of some integrals over an unbounded integral whose integrand decays rather slowly which implies that their numerical handling is difficult and costly. We present a novel variant of such a diffusive representation. This form also requires the numerical approximation of an integral over an unbounded domain, but the integrand decays much faster. This allows to use well established quadrature rules with much better convergence properties.
