Lectures related to Hyperbolic Problems: Transport Equation

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Numerical Modelling of the Atmosphere

Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Wave Equations: Vibrating String

Explores the wave equation for a vibrating string and its numerical solution using finite difference formulas and the Newmark scheme in MATLAB/GNU Octave.

Cauchy Problem Resolution: General Solution Approach

Covers the resolution of a Cauchy problem using a general solution approach for differential equations.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Linear Differential Equations: Constant Coefficients and Solution Methods

Covers linear differential equations with constant coefficients and introduces the method of good choice for finding particular solutions.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's definition interval.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Euler Method: Understanding Higher Order Runge-Kutta Schemes

Explains the Euler method and higher-order Runge-Kutta schemes for solving differential equations.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Introduction to Numerical Methods for PDEs

Covers the numerical approximation of PDEs and examples of nonlinear behavior.

Finite Difference Methods: Stability Analysis

Explores the stability analysis of finite difference methods for solving differential equations.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Higher Order Schemes

Explores higher-order schemes for solving differential equations and their stability analysis compared to other methods.