054361 - Metodi Analitici e Numerici per l'Ingegneria

A collection of modular MATLAB scripts implementing core numerical analysis algorithms for solving engineering problems.

Numerical solution of a Cauchy-Dirichlet problem for a parabolic PDE using a non-complete Fourier Series expansion.

Overview

The repository is structured to be simple and modular. The labs directory contains the main lab scripts (Lab*.m), each corresponding to a specific topic or problem set. The core logic is housed in the functions/ directory, which contains a set of reusable MATLAB functions.

Key implemented algorithms include:

• Root-finding: Bisection, Newton's method, Fixed-point iteration.
• Linear Systems: Thomas algorithm for tridiagonal systems, Forward/Backward substitution.
• Eigenvalue Problems: Power method and Inverse power method.
• Numerical Integration: Composite Trapezoidal and Simpson's rules.
• ODEs: Euler (forward and backward), Heun, Crank-Nicolson, and a general Theta-method implementation.
• PDEs/Finite Elements: Solvers for diffusion and reaction-diffusion problems using Finite Element methods.
• Iterative Methods: Richardson, Gradient method.

The img/ directory contains plots and diagrams generated from the lab scripts, visually representing the results of the simulations.

Quick Start Guide

To run these scripts, you will need a working installation of MATLAB or GNU Octave. Simply clone the repository and navigate to the labs directory to execute the lab scripts.

You will also need to add the functions/ directory to your MATLAB path to ensure that all functions are accessible.

addpath('functions');

Examples of Simulations

The scripts produce a variety of numerical solutions, often visualized as plots. Here are a couple of examples from the collection.

Satellite Trajectory Simulation

Numerical integration of a satellite trajectory under the influence of Earth's gravity and hypothetical air resistance.

Simulation of the satellite trajectory approaching Earth

SEIR Model for Epidemic Spread

A simulation of a Susceptible-Exposed-Infected-Recovered (SEIR) model, a common model in epidemiology.

SEIR model with a beta coefficient variable over time (the beta variable is the infection rate)

Galerkian Method Application

A simple application of the Galerkian method to a linear elastic element.

Simple application of the Galerkian method to a linear elastic element

Have a nice coding day,

Tommaso 🐼