QGLAB: A MATLAB Package for Computations on Quantum Graphs

Abstract

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 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.

Publication
QGLAB: A MATLAB Package for Computations on Quantum Graphs
Roy Goodman
Roy Goodman
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

My research interests include dynamical systems and nonlinear waves, vortex dynamics, quantum graphs, and network inference

Gracie Conte
Gracie Conte
Senior Professional Staff I