论文标题
分析一种新型的分数线性多步数方法的阶级两种方法，并具有改善的稳定性
Analysis of a new type of fractional linear multistep method of order two with improved stability
论文作者
论文摘要
我们介绍并研究了一种新型的隐式分数线性多步数方法，用于分数初始值问题。该方法是从分数衍生物在非倾斜移位点处的grünwald-letnikov近似的二阶超级收敛获得的。所提出的方法是两个一致性的阶，并且与衍生物的顺序为一个时，与经典初始值问题的后退差异方法相吻合。该方法的重量系数是从Grünwald的重量获得的，因此与二级阶的分数向后差公式相比，计算有效的效率。分析了稳定性，并表明该方法的稳定性区域大于二级和分数梯形方法的分数Adams-Moulton方法的稳定性区域。提出了数值结果和插图以证明分析理论的合理性。
We present and investigate a new type of implicit fractional linear multistep method of order two for fractional initial value problems. The method is obtained from the second order super convergence of the Grünwald-Letnikov approximation of the fractional derivative at a non-integer shift point. The proposed method is of order two consistency and coincides with the backward difference method of order two for classical initial value problems when the order of the derivative is one. The weight coefficients of the proposed method are obtained from the Grünwald weights and hence computationally efficient compared with that of the fractional backward difference formula of order two. The stability properties are analyzed and shown that the stability region of the method is larger than that of the fractional Adams-Moulton method of order two and the fractional trapezoidal method. Numerical result and illustrations are presented to justify the analytical theories.
