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.
A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.
Basic notebook covering how to implement Euler's method, without much focus on theory
Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.
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.
Computing the trajectory of a projectile moving through the air, subject to wind and air drag.
Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.
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.
Using a forward-shooting method to determine the eigenenergies and eigenfunctions of an asymmetric potential in one dimension.
Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.
Using the method of forward shooting to determine numerically the eigenenergies of the quantum harmonic oscillator in one dimension.
Computing planet Mars' atmospheric pressure profile from its temperature profile.
Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.
Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.
Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.
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.
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).
Numerical integration in D dimensions using the Monte Carlo method.
Numerical integration in one dimension using the Monte Carlo method.
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.