We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations) and more. It overcomes the major challenge of discretizing quantum graphs -- the enforcement of vertex conditions -- using non-square differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class.

翻译：本文介绍QGLAB，一个用于分析量子图上偏微分方程的新型MATLAB软件包。该软件基于现有的面向对象MATLAB有向图类构建，继承了其结构并增加了易于使用的附加功能。该软件包允许用户构建量子图，并精确计算椭圆算子的谱、泊松问题的解、各类偏微分方程的线性和非线性时间演化、稳态解分支的延拓（包括在分岔点定位与切换分支）等功能。它通过使用非方形微分矩阵，克服了离散化量子图的主要挑战——顶点条件的强制实施。该软件包采用统一框架实现量子图上微分算子的有限差分和切比雪夫离散化。为简化操作，软件包重载了许多内置MATLAB函数以适配该类别。