MartinMikkelsen/ppnmJulia

Practical Programming and Numerical Methods in Julia

This repository contains a collection of scripts written in Julia, demonstrating various numerical methods and machine learning techniques. The scripts are organized into two main directories:

1. differential_equations/: This directory contains scripts that solve various differential equations using different methods. Here are the scripts you'll find in this directory:

   • Belousov–Zhabotinsky.jl: This script models the Belousov-Zhabotinsky reaction, a classic example of a non-equilibrium chemical oscillator.
   • FitzHugh-Nagumo.jl:
   • HeatEquation.jl: This script solves the heat equation, a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
   • Hénon-Heiles.jl:
   • Runge-Kutta.jl:

2. numerical_methods/: This directory contains scripts that implement various numerical methods. Here are the scripts you'll find in this directory:

   • Cholesky_decomposition.jl: This script implements the Cholesky decomposition method, a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose.
   • Clenshaw-Curtis.jl:
   • Conjugate_gradient.jl: This script implements the conjugate gradient method, an algorithm for the numerical solution of particular systems of linear equations.
   • Gradient_decent.jl: This script implements the gradient descent optimization algorithm.
   • bisection.jl: This script implements the bisection method, a root-finding method that applies to any continuous function.