Search: differential equation

10 results

Mechanics 1

  Double Pendulum and Chaos

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

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

Astrophysics 1

Partial Differential Equations 3

  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

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.

  Iterative Gauss-Seidel Method

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.

Ordinary Differential Equations 5

  Adaptive Runge-Kutta Methods

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

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

  Runge-Kutta Methods

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

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).

  Euler's Method

ode, explicit euler method

Solving a first-order ordinary differential equation with Euler's method.

  Verlet Integration

ode

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