Numerical Derivation: Formulas and Approaches

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Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Error Estimation in Numerical Methods

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

Numerical Differentiation: Part 1

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

Runge-Kutta Methods: Approximating Differential Equations

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

Convergence Analysis: Explicit RK Scheme

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

Crank-Nicolson and Heun's Methods

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

Euler Method: Understanding Higher Order Runge-Kutta Schemes

Explains the Euler method and higher-order Runge-Kutta schemes for solving differential equations.

High Order Methods: Space Discretisation

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

Euler Forward Method

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

Multigroup Theory: Main Equations and Numerical Solution

Covers the derivation of multi-group diffusion equations and the numerical methods for solving the neutron diffusion equation.