Nonlinear quantum graphs are metric graphs equipped with a nonlinear Schr{\"o}dinger equation. Whereas in the last ten years they have known considerable developments on the theoretical side, their study from the numerical point of view remains in its early stages. The goal of this paper is to present the Grafidi library, a Python library which has been developed with the numerical simulation of nonlinear Schr{\"o}dinger equations on graphs in mind. We will show how, with the help of the Grafidi library, one can implement the popular normalized gradient flow and nonlinear conjugate gradient flow methods to compute ground states of a nonlinear quantum graph. We will also simulate the dynamics of the nonlinear Schr{\"o}dinger equation with a Crank-Nicolson relaxation scheme and a Strang splitting scheme. Finally, in a series of numerical experiments on various types of graphs, we will compare the outcome of our numerical calculations for ground states with the existing theoretical results, thereby illustrating the versatility and efficiency of our implementations in the framework of the Grafidi library.
翻译：非线性量子图是带有非线性 Schr } o}dinger 方程式的矩阵图。 在过去的十年中,他们知道理论方面有相当大的发展,但是他们从数字角度的研究仍处于早期阶段。本文的目的是展示Grafidi 库,这是一个Python 库,它是在图形中以非线性 Schr \"o}deder 方程式的数字模拟方式开发的。我们将在格拉菲迪 库的帮助下,展示如何在现有的理论结果下,实施流行的标准化梯度流和非线性梯度流法,以计算非线性量度图的地面状态。我们还将用Crank-Nicolson 放松计划和Strang 分裂方案模拟非线性 Schr r o} 等式等式的动态。最后,在一系列关于各种图表的数值实验中,我们将将我们计算地面状态的数字结果与现有的理论结果进行比较,从而显示我们在Grafididi 图书馆框架中执行的多用途和效率。
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