A Functional Package for Automatic Solution of Ordinary Differential Equations with Spectral Methods

TL;DR

This paper introduces PyCheb, a Python module that automates the spectral collocation method for solving ordinary differential equations with high precision, including discretization, interpolation, and solution visualization.

Contribution

The paper presents PyCheb, a novel Python package that simplifies and automates spectral collocation solutions for ODEs, integrating discretization, interpolation, and automatic resolution determination.

Findings

PyCheb achieves high-precision solutions for ODEs.

The module automates discretization and visualization processes.

Users can easily specify boundary conditions and parameters.

Abstract

We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this Python module, users can initialize the ODEsolver class by passing attributes, including the both sides of a given differential equation, boundary conditions, and the number of Chebyshev points, which can also be generated automatically by the ideal precision, to the constructor of ODEsolver class. Then, the instance of the ODEsolver class can be used to automatically determine the resolution of the differential equation as well as generate the graph of the high-precision approximate solution. (If you have any questions, please send me an email and I will reply ASAP. e-mail:shaohui_liu@qq.com/2013141482143@stu.scu.edu.cn)