Cauchy Problem: Euler Methods

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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.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Implicit Euler Scheme

Explains the Implicit Euler Scheme, a method for solving differential equations numerically, focusing on stability and convergence properties.

Predictor-Corrector Method: Harmonic Oscillator

Explores the Predictor-Corrector method for the harmonic oscillator and Runga-Kutta method in differential equations.

Runge Kutta and Multistep Methods

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

Direction Fields, Euler Methods, Differential Equations

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

Numerical Methods: Euler Schemes

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