Lectures related to Multistep methods

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.

Ordinary Differential Equations: Methods and Accuracy

Introduces methods for solving ordinary differential equations and discusses their accuracy and limitations.

Differential Equations: Solution Methods MOOC: Electrical engineering II

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Implicit Euler Scheme

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

Ordinary Differential Equations: Methods and Applications

Explores ordinary differential equations and numerical integration methods for stability and accuracy.

Runge-Kutta Methods: Approximating Differential Equations

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

Numerics: semester project

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

High Order Methods: Space Discretisation

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

Cauchy Problem Resolution: Differential Equations Overview

Covers the resolution of a Cauchy problem for a first-order linear differential equation, detailing the construction of its general solution and the determination of initial conditions.

Predictor-Corrector Method: Harmonic Oscillator

Explores the Predictor-Corrector method for the harmonic oscillator and Runga-Kutta method in 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.

Error Estimation in Numerical Methods Log in to Mediaspace to watch this video

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

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

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

System of ODEs Log in to Mediaspace to watch this video

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

Runge Kutta and Multistep Methods Log in to Mediaspace to watch this video

Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4 Log in to Mediaspace to watch this video

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Numerical Integration: Euler Method Log in to Mediaspace to watch this video

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.

Ordinary Differential Equations: Non-linear Analysis Log in to Mediaspace to watch this video

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Error Estimation in Numerical Methods Log in to Mediaspace to watch this video

Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.

Direction Fields, Euler Methods, Differential Equations Log in to Mediaspace to watch this video

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.