trapezoidal method, waves, Fourier transform
An introduction to studying linear surface waves on an infinite domain. In particular, the problem of finding the time evolution of a small perturbation of the surface of an inviscid and incompressible fluid.
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.
explicit euler method, ode, implementation, basic
Basic notebook covering how to implement Euler's method, without much focus on theory
magnetism, explicit euler method, ode, Lorentz' law
Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.
animation, 4th order runge-kutta, system of equations
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.
explicit euler method, 4th order runge-kutta, ode, Big Bertha, set of odes
Computing the trajectory of a projectile moving through the air, subject to wind and air drag.
animation, gravity, newton, semi-implicit euler method
Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.
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.
schrödinger equation, bloch's theorem, newton's theorem
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.
simpson's method, temperature, pressure
Computing planet Mars' atmospheric pressure profile from its temperature profile.
simpson's method, newton, euler, eigenvalue, poisson's equation, integration, interpolation
Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.
animation, space, gravity, newton, embedded runge-kutta pair, angular momentum
Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.
space, explicit euler method, gravity, newton
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.
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.
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.
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.
explicit euler method, 4th order runge-kutta, ode
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).
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.
Numerical integration using the trapezoidal and Simpson's rules.
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Physical courses: NumFys kurs (Norwegian)
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