jaantollander / LegendreSeries

Python code for studying the convergence of Legendre series for piecewise analytic functions.

Legendre Series for Piecewise Analytic Functions

This repository is related to my article Exploring the Pointwise Convergence of Legendre Series for Piecewise Analytic Functions.

Contents

• legendre_series.py contains the code for computing the Legendre series and analysing the pointwise convergence.
• plots.py contains the code for plotting the results from the computations.
• scripts directory contains script files for creating the different plots.

Instructions

Install Miniconda (or Anaconda).

Install Conda environment

conda env create -f environment.yml 

Activate the environment

source activate legendre36

Create the figures

python scripts/run_legendre_polynomials.py
python scripts/run_piecewise_functions.py
python scripts/run_legendre_series.py
python scripts/run_pointwise_convergence.py
python scripts/run_convergence_distance.py

Additionally, creating the animations requires FFmpeg.

python scripts/run_animation.py