newton, animation, semi-implicit euler method, gravity

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

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

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

animation, ode, explicit euler method

Simulates the simple pendulum and damped simple pendulum

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

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.

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.

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.

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.

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

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

A study of the trajectory of a ball that is moving through the air, subject to air drag and wind.

explicit euler method, lennard-jones potential

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