Numerical Methods: Differential Equations and Stability Analysis

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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.

Finite Difference Methods: Stability Analysis

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

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.

Euler Forward Method

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.

High Order Methods: Space Discretisation

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

Cauchy Problem Resolution: General Solution Approach

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

Direction Fields, Euler Methods, Differential Equations

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

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.