This paper analyzes the numerical stability of a class of two-step spline collocation methods for initial value problems for fractional differential equations. The stability region is characterized in terms of the eigenvalues of a power series, which depends on the method parameters. We provide the stability regions for several choices of the method parameters. Numerical experiments prove the effectiveness of the stability results both in a constant stepsize framework and in the case of graded meshes.

中文翻译：

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分数阶微分方程初值问题两步样条搭配法的稳定性

本文分析了一类两步样条搭配法求解分数阶微分方程初值问题的数值稳定性。稳定区域的特征在于幂级数的特征值，这取决于方法参数。我们为方法参数的几种选择提供了稳定区域。数值实验证明了在恒定步长框架和分级网格情况下稳定性结果的有效性。