A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.
Basic notebook covering how to implement Euler's method, without much focus on theory
Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.
Computing the trajectory of a projectile moving through the air, subject to wind and air drag.
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).
A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.