Abstract In this paper, we propose an unconditionally stable numerical scheme based on finite difference for the approximation of time-fractional diffusion equation on a metric star graph. The fractional derivative is considered in Caputo sense and the so-called L1 method is used for the discrete approximation of Caputo fractional derivative. The convergence and stability of the difference scheme has been proved by means of energy method. Test examples are illustrated in order to verify the feasibility of the proposed scheme.

中文翻译：

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度量星图上时间分数扩散方程的差分格式

摘要 在本文中，我们提出了一种基于有限差分的无条件稳定数值方案，用于逼近度量星图上的时间分数扩散方程。在 Caputo 意义上考虑分数阶导数，所谓的 L1 方法用于 Caputo 分数阶导数的离散逼近。用能量法证明了差分格式的收敛性和稳定性。举例说明，以验证所提出的方案的可行性。