Lectures related to Hyperbolic Transport Equations

High Order Methods: Space Discretisation

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

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Runge-Kutta Methods: Approximating Differential Equations

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

Implicit Euler Scheme

Explains the Implicit Euler Scheme, a method for solving differential equations numerically, focusing on stability and convergence properties.

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Numerical Analysis: Implicit Schemes

Covers implicit schemes in numerical analysis for solving partial differential equations.

Finite Differences Method: Error Division and Schemes MOOC: Numerical Analysis for Engineers

Covers error division and schemes for solving differential equations.

Computational Geomechanics: Unconfined Flow

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

Numerics: semester project

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

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.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Wave Equation: Numerical Methods

Explores numerical methods for solving the wave equation, discussing stability conditions and convergence rates.

Convergence Analysis: Explicit RK Scheme

Explores the convergence analysis of the Explicit Runge-Kutta scheme for accurate numerical solutions.

Numerical Methods: Euler and Crank-Nicolson Log in to Mediaspace to watch this video

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

Numerical Analysis: Stability in ODEs Log in to Mediaspace to watch this video

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