This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity preservation of the explicit L1-scheme, it is shown that for sufficiently small initial values, numerical solutions exist globally. Whereas for large initial values, numerical solutions with a suitable adaptive step strategy blow up in finite time. Finally, some numerical experiments are provided for verifying the theoretical analysis.

中文翻译：

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分数阶常微分方程显式L1格式的数值爆破分析

本文研究具有耗散项的非线性分数阶常微分方程数值解的爆破行为。基于显式L1方案的正性保留，表明对于足够小的初始值，全局存在数值解。对于较大的初始值，具有合适的自适应步长策略的数值解会在有限的时间内爆炸。最后，提供了一些数值实验来验证理论分析。