Lectures related to Explicit RK Methods

High Order Methods: Space Discretisation

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

Advanced Numerical Analysis: Space Discretization

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

Runge-Kutta Methods: Approximating Differential Equations

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

Numerical Analysis: Stability in ODEs

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

Runge Kutta and Multistep Methods

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

Numerical Methods: Euler and Crank-Nicolson

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

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Convergence Analysis: Explicit RK Scheme

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

Numerics: semester project

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Homogeneous Solutions: Linear Independence

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Phase Portrait and Non-linear Systems

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

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.

Crank-Nicolson and Heun's Methods

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Runge-Kutta Methods

Explains the Runge-Kutta methods, particularly the explicit scheme of order 4 (ERK4), and how to optimize parameters for accuracy.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

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.

System of ODEs

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

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.