Euler's Method

euler, differential equation, euler explicit method, set of odes, basic

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

  Double Pendulum and Chaos

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

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

  General Relativity

space, einstein, gravity, newton, 4th order runge-kutta, angular momentum, differential equation, ode

Discussion of orbits in the Schwarzschild Geometry.

  Relaxation Methods for Solving PDE's

poisson's equation, iterative, laplace's equation, uniqueness theorem

The Jacobi, Gauss-Seidel and Successive overrelaxation (SOR) methods are introduced and discussed with the Poisson equation as an example.

  Partial Differential Equations - Two Examples

animation, laplace's equation, finite-differences, pde, differential equation, stability, implicit euler method

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

  Iterative Gauss-Seidel Method

sparse matrix, system of equations, iterative, laplace's equation, pde, differential equation, gauss

Solves a linear of system of equations using the iterative Gauss-Seidel method.

  Adaptive Runge-Kutta Methods

explicit euler method, 4th order runge-kutta, embedded runge-kutta pair, trapezoidal method, ode

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

  Runge-Kutta Methods

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

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

  Implicit Euler Method

euler, ode

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

  Verlet Integration

ode

Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.