Error Estimation in Numerical Methods

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Runge-Kutta Methods: Approximating Differential Equations

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

Finite Difference Methods: Stability Analysis

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

Euler Forward Method

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

Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

Numerical Methods: Euler Schemes

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

Numerical Methods: Differential Equations and Stability Analysis

Covers numerical methods for solving differential equations and their stability analysis, focusing on error calculation and practical applications in engineering and science.

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.

Numerical Differentiation: Part 1

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

Convergence: Euler's Method

Explores stability and convergence in numerical methods for ODEs, focusing on Euler's progressive method.

High Order Methods: Space Discretisation

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