Euler's Method

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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

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

  Uniform Magnetic Field

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

  Projectile motion

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

  Simple Pendulum

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Simulates the simple pendulum and damped simple pendulum

  Planetary Motion

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

  Adaptive Runge-Kutta Methods

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

  Runge-Kutta Methods

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

  Lennard-Jones Potential

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