Search: euler

15 results

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

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.

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 1

  Gravity Assist

newton, animation, semi-implicit euler method, gravity

Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.

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

Fluid Mechanics 1

  Euler Equations for Inviscid Flow

An introduction to the compressible Euler equations and methods for solving them numerically.

Waves and Acoustics 1

  Sloshing

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.

Astrophysics 1

  Planetary Motion

newton, space, explicit euler method, gravity

Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.

Partial Differential Equations 1

  Partial Differential Equations - Two Examples

differential equation, stability, implicit euler method, animation, laplace's equation, finite-differences, pde

This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.

Ordinary Differential Equations 4

  Adaptive Runge-Kutta Methods

4th order runge-kutta, 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).

  Euler's Method

ode, explicit euler method

Solving a first-order ordinary differential equation with Euler's method.

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.