## 15 results

#### Euler's Method

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

#### Simple implementation of Euler's method

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

#### Uniform Magnetic Field

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

#### Projectile motion

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

#### Gravity Assist

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

#### Double Pendulum and Chaos

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

#### Simple Pendulum

Simulates the simple pendulum and damped simple pendulum

#### Euler Equations for Inviscid Flow

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

#### Sloshing

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

#### Planetary Motion

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 - Two Examples

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

#### Adaptive Runge-Kutta Methods

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

#### Runge-Kutta Methods

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

#### Implicit Euler Method

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

#### Lennard-Jones Potential

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