A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.
The trajectory of a charged particle propagating in a non-uniform magnetic field is calculated by solving the Lorentz force law using an embedded Runge-Kutta pair. The results show that the particle is mirrored.
Basic notebook covering how to implement Euler's method, without much focus on theory
Using the Metropolis algorithm to approximate the magnetization and specific heat for a 2D Ising lattice.
Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.
Solving the time independent Schrödinger equation in one dimension using matrix diagonalisation for five different potentials.
Computing the trajectory of a projectile moving through the air, subject to wind and air drag.
Discussion of orbits in the Schwarzschild Geometry.
Uses cubic splines to interpolate a given set of data points
Solving the one-dimensional stationary heat equation with a Gaussian heat source by approximating the solution as a sum of Lagrange polynomials.
Simulates the disentanglement of a polymer from a surface using an increasing electric field
Computing the internal energy, specific heat and magnetisation in the 1D and 2D Ising model. An analytical solution to the XY model is also provided.
Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.
Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.
Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.
Solving a first-order ordinary differential equation using the Runge-Kutta method.
Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).
Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.
A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.