## 30 results

#### Linear Wave Propagation

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's Method

A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.

#### Simple implementation of Euler's method

Basic notebook covering how to implement Euler's method, without much focus on theory

#### Uniform Magnetic Field

Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.

#### Stabilising an Inverted Pendulum on a Cart

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.

#### Projectile motion

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

#### Gravity Assist

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

#### Simple Pendulum

Simulates the simple pendulum and damped simple pendulum

#### Relaxation Methods for Solving PDE's

The Jacobi, Gauss-Seidel and Successive overrelaxation (SOR) methods are introduced and discussed with the Poisson equation as an example.

#### Fixed-Point Iteration

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

#### Euler Equations for Inviscid Flow

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

#### Numerical Determination of Eigenenergies for an Asymmetric Potential

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

#### Band Structures and Newton's Method

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

#### Numerical Determination of Eigenenergies for the Harmonic Oscillator

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

#### Martian Atmosphere

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

#### Sloshing

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

#### Planetary Motion - Three Body Problem

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

#### Planetary Motion

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

#### Calling Fortran(95) Routines from a Python Script

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.

#### Partial Differential Equations - Two Examples

This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.

#### Iterative Gauss-Seidel Method

Solves a linear of system of equations using the iterative Gauss-Seidel method.

#### Ordinary Differential Equations 3

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

#### Runge-Kutta Methods

Solving a first-order ordinary differential equation using the Runge-Kutta method.

#### Implicit Euler Method

Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).

#### Newton-Raphson Method

Determining a root with the Newton-Raphson algorithm.

#### Monte Carlo Integration in D Dimensions

Numerical integration in D dimensions using the Monte Carlo method.

#### Monte Carlo Integration in One Dimension

Numerical integration in one dimension using the Monte Carlo method.

#### Lennard-Jones Potential

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

#### Bisection Method

Determining a root using the bisection method.

#### Numerical Integration

Numerical integration using the trapezoidal and Simpson's rules.