Lectures related to Runge-Kutta 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.

Runge-Kutta Methods: Approximating Differential Equations

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

Numerical Methods: Euler and Crank-Nicolson

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

System of ODEs

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

Multistep methods

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Optimization methods

Covers optimization methods, focusing on gradient methods and line search techniques.

Numerics: semester project

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

Runge Kutta and Multistep Methods

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

High Order Methods: Space Discretisation

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

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Advanced Numerical Analysis: Space Discretization

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

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

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

Zero-stability and absolute-stability

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

Explicit RK Methods

Explains explicit Runge-Kutta methods up to order 4 and conditions for method's order.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Energy Systems Optimization

Explores energy systems modeling, optimization, and cost analysis for efficient operations.

Ordinary Differential Equations: Error Analysis

Explores error analysis in ordinary differential equations and convergence criteria for numerical methods.

Wave Equation: Numerical Methods

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

Ordinary Differential Equations: Methods and Applications

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