In my research I mostly work with the Julia programming language and most of the software I produce tends to be different kinds of Julia packages. You can find most of my packages on GitHub, some of the more important ones are also listed below.

# Arblib.jl

Arblib is a Julia package in the public repository which aims to be a thin and efficient wrapper around Arb - a C library for arbitrary-precision ball arithmetic. I’m one of the main developers, together with Marek Kaluba and Sascha Timme.

# ArbExtras.jl

ArbExtras is a Julia package that extends Arblib with basic tools for rigorous numerics that I found useful in many of my projects. Among other things it contains methods for isolating roots and computing extrema of functions. It is not in the public Julia repository and there is currently no general documentation, though individual methods are usually well documented.

# MethodOfParticularSolutions.jl

A Julia package for computing eigenvalues and eigenfunctions of the Laplacian on planar or spherical domains using the method of particular solutions. This package has mainly been written for use in specific projects and is not very suitable for general usage.

- Dahne, J., Gómez-Serrano, J., & Hou, K. (2021). A counterexample to Payne’s nodal line conjecture with few holes. Commun. Nonlinear Sci., 103(), 105957.
- Dahne, J., & Salvy, B., Computation of tight enclosures for laplacian eigenvalues, SIAM Journal on Scientific Computing, 42(5), 3210–3232 (2020).

# PaynePolygon.jl

The computer assisted proof accompanying the paper

Dahne, J., Gómez-Serrano, J., & Hou, K. (2021). A counterexample to Payne’s nodal line conjecture with few holes. Commun. Nonlinear Sci., 103(), 105957.

# BurgersHilbertWave.jl

The computer assisted proof accompanying the paper

Dahne, J. & Gómez-Serrano J. (2023). Highest Cusped Waves for the Burgers-Hilbert Equation. Archive for Rational Mechanics and Analysis, 247(5).

# HighestCuspedWave.jl

The computer assisted proof accompanying the paper

Dahne, J. (2023). Highest Cusped Waves for the Fractional KdV Equations.