Error Estimation in Numerical Methods

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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.

Numerical Differentiation: Part 1

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

High Order Methods: Space Discretisation

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

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 Modelling of the Atmosphere

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

Runge-Kutta Methods: Approximating Differential Equations

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

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.

Euler Forward Method

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

Consistency and Stability in Numerical Methods

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.