Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.
An introduction to the compressible Euler equations and methods for solving them numerically.
Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.
Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.
This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.
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 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.
A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.