Search: ode

23 results

Ordinary Differential Equations 1

  Euler's Method

differential equation, euler, basic, euler explicit method, set of odes

A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.

Electromagnetism 1

  Magnetic Mirror

embedded runge-kutta pair, integration, set of 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.

Basics 1

  Simple implementation of Euler's method

implementation, basic, ode, explicit euler method

Basic notebook covering how to implement Euler's method, without much focus on theory

Statistical Mechanics 1

  Equilibrium Monte Carlo simulation of the 2D Ising model

magnetism, metropolis, equilibrium, autocorrelation, ising, monte carlo, spin, fortran, f2py

Using the Metropolis algorithm to approximate the magnetization and specific heat for a 2D Ising lattice.

Electromagnetism 1

  Uniform Magnetic Field

magnetism, Lorentz' law, ode, explicit euler method

Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.

Quantum Mechanics 1

  Modeling Atoms, Molecules, and Crystals in One Dimension

eigenenergy, eigenstate, schrödinger equation, waves, spin, hemmer

Solving the time independent Schrödinger equation in one dimension using matrix diagonalisation for five different potentials.

Mechanics 1

  Projectile motion

4th order runge-kutta, Big Bertha, ode, explicit euler method, set of odes

Computing the trajectory of a projectile moving through the air, subject to wind and air drag.

Astrophysics 2

  The Fate of Our Universe

space, ode, gravity

Solving the Friedmann equations to model the expansion of our universe.

  Precession of Mercury

ode, gravity, 4th order runge-kutta, einstein, angular momentum, space, fortran, extrapolation, f2py

Computes the precession of Mercury by linear extrapolation.

Mechanics 2

  Double Pendulum and Chaos

differential equation, animation, Lagrangian, Euler-Lagrange equations, chaos, phase space, odeint

Discusses the chaotic motion of the double pendulum using a phase-space diagram

  Simple Pendulum

animation, ode, explicit euler method

Simulates the simple pendulum and damped simple pendulum

Astrophysics 1

Curve Fitting 1

Thermodynamics 1

  One-dimensional Stationary Heat Equation

chebychev nodes, temperature

Solving the one-dimensional stationary heat equation with a Gaussian heat source by approximating the solution as a sum of Lagrange polynomials.

Biophysics 1

  The Fiber Bundle Bridge Model

polymer, hemmer, hansen, lennard-jones potential, sparse matrix, nygård, elasticity

Simulates the disentanglement of a polymer from a surface using an increasing electric field

Statistical Mechanics 1

  Ising Model in 1D and 2D

specific heat, partition function, magnetism, spin

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.

Waves and Acoustics 1


euler, eigenvalue, poisson's equation, integration, interpolation, newton, simpson's method

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

Curve Fitting 1

  Polynomial Interpolation

chebychev nodes, newton, interpolation, lagrange, runges phenomenon

Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.

Ordinary Differential Equations 4

  Adaptive Runge-Kutta Methods

4th order runge-kutta, embedded runge-kutta pair, trapezoidal method, ode, explicit euler method

Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.

  Runge-Kutta Methods

4th order runge-kutta, ode, explicit euler method

Solving a first-order ordinary differential equation using the Runge-Kutta method.

  Implicit Euler Method

euler, ode

Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).

  Verlet Integration


Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.

Chemistry 1

  Lennard-Jones Potential

explicit euler method, lennard-jones potential

A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.