Lecture
Error Estimation in Numerical Methods
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Error Estimation in Numerical Methods
Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.
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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 Integration: Euler Method
Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.
Runge-Kutta Methods: Approximating Differential Equations
Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.
High Order Methods: Space Discretisation
Covers high order methods for space discretisation in linear differential systems.
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.
Numerical Analysis: Stability in ODEs
Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.
Ordinary Differential Equations: Non-linear Analysis
Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.
Direction Fields, Euler Methods, Differential Equations
Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.