4th order runge-kutta, system of equations, animation

The 4th order Runge-Kutta method was used to integrate the equations of motion for the system, then the pendulum was stabilised on its inverted equilibrium point using a proportional gain controller and linear quadratic regulator.

4th order runge-kutta, Big Bertha, ode, explicit euler method, set of odes

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

newton, animation, semi-implicit euler method, gravity

Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.

animation, ode, explicit euler method

Simulates the simple pendulum and damped simple pendulum

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.

Solving fixed-point problems using the Fix-Point Iteration method.

An introduction to the compressible Euler equations and methods for solving them numerically.

eigenenergy, forward shooting, eigenstate, schrödinger equation

Using a forward-shooting method to determine the eigenenergies and eigenfunctions of an asymmetric potential in one dimension.

bloch's theorem, newton's theorem, schrödinger equation

Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.

eigenenergy, harmonic oscillator, forward shooting, eigenstate

Using the method of forward shooting to determine numerically the eigenenergies of the quantum harmonic oscillator in one dimension.

temperature, pressure, simpson's method

Computing planet Mars' atmospheric pressure profile from its temperature profile.

euler, eigenvalue, poisson's equation, integration, interpolation, newton, simpson's method

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

animation, gravity, newton, embedded runge-kutta pair, angular momentum, space

Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.

newton, space, explicit euler method, gravity

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

electricity, fortran, trapezoidal method

Making use of the Fortran to Python package F2PY which enables creating and compiling a Fortran routine before converting it to a Python Module, which can be imported to any Python script.

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

Numerical integration in D dimensions using the Monte Carlo method.

Numerical integration in one dimension using the Monte Carlo method.

explicit euler method, lennard-jones potential

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

Determining a root using the bisection method.

Numerical integration using the trapezoidal and Simpson's rules.