A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.
Discusses the chaotic motion of the double pendulum using a phase-space diagram
Discussion of orbits in the Schwarzschild Geometry.
The Jacobi, Gauss-Seidel and Successive overrelaxation (SOR) methods are introduced and discussed with the Poisson equation as an example.
This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.
Solves a linear of system of equations using the iterative Gauss-Seidel method.
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).
Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.