linear-systems-analysis

ODE linear systems with plots and phase portraits.

This project provides a tool to analyze 2D linear systems of differential equations. It compares numerical solutions from 'odeint' with the exact solutions generated by matrix exponential.

Note:

This is a personal educational project, created to test out Python visualization of linear dynamics. The code is a work in progress. Eventually, I plan to refine the structure and add more features. Since this repository is a sandboc for my ODE solver experiments, the code may not be fully optimized. I may make frequent changes as I go.

Mathematical Overview

The system is defined by: $$\mathbf{\dot{x}} = A\mathbf{x}$$

The behavior of the trajectories is determined by the trace and determinant of the matrix $A$.

There is a colab notebook on the first Weyl Algebra, talking about odes from a rings/modules perspective. I did not proofread it before uploading; just be aware there may be errors.

Features

• Phase Portraits Plots vector fields and steamlines.
• • Interactive Visualization: Uses ipywidgets to change matrix parameters on the fly.