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

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

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

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

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

Discussion of orbits in the Schwarzschild Geometry.

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.

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

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

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

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

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

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

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

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