Crank-Nicolson and Heun's Methods

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Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

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 Integration: Trapezoidal Rule

Covers numerical integration methods, focusing on the trapezoidal rule and iterative processes.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

High Order Methods: Space Discretisation

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

Runge-Kutta Methods: Approximating Differential Equations

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