Lectures related to Newton Method: Nonlinear Equations

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Nonlinearity: Methods and Examples

Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.

Newton's Method: Order 2

Explains Newton's method of order 2 for finding function zeros.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Newton's Method: Fixed Point Iterative Approach

Covers Newton's method for finding zeros of functions through fixed point iteration and discusses convergence properties.

Newton's Method: Convergence

Explores the convergence of Newton's method for solving nonlinear equations and the importance of selecting appropriate initial guesses.

Nonlinear Equations: Methods and Applications

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Numerical Analysis: Newton's Method

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Jacobi and Gauss-Seidel methods

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Numerical Methods: Fixed Point and Picard Method

Covers fixed point methods and the Picard method for solving nonlinear equations iteratively.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Numerical Analysis: Nonlinear Equations

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Crank-Nicolson and Heun's Methods

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Newton's Method: Convergence and Applications

Covers the convergence of Newton's method and its applications in numerical analysis.

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.

Stopping Criteria for Nonlinear Equations

Discusses stopping criteria for fixed point iteration and Newton's method in nonlinear equations.