论文标题
分数订单runge-kutta方法
Fractional Order Runge-Kutta Methods
论文作者
论文摘要
本文研究了一种新的分数runge-kutta（叉）方法，用于数值近似于分数微分方程（FDES）的溶液。通过使用Caputo GeneralizedTaylor公式和Caputo分数衍生物的总差异，我们将构建明确和隐式的前叉方法作为普通微分方程的众所周知的Runge-Kutta方案。在提出的方法中，由于分数衍生物对固定基点$ T_0的依赖性，我们必须在叉子方法的所有步骤中修改给定方程的右侧。提出了一些明确和隐式前叉方案的系数。还讨论了该方法的收敛分析。数值实验阐明了该方法的有效性和鲁棒性。
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total differential for Caputo fractional derivative, we construct explicit and implicit FORK methods, as the well-known Runge-Kutta schemes for ordinary differential equations. In the proposed method, due to the dependence of fractional derivatives to a fixed base point $t_0,$ we had to modify the right-hand side of the given equation in all steps of the FORK methods. Some coefficients for explicit and implicit FORK schemes are presented. The convergence analysis of the proposed method is also discussed. Numerical experiments clarify the effectiveness and robustness of the method.
