Course

MATH-351: Advanced numerical analysis II

Lectures in this course (51)

Covers the concept of order of accuracy in numerical methods and its implications on final results.

Provides an overview of Runge-Kutta methods for solving ODEs of order 4.

Covers the Runge-Kutta method and its variations, discussing error minimization and stability in non-linear systems.

Explores the Conjugate Gradient method for solving linear systems and introduces Quasi-Newton methods and rank 2 updates.

Explains the Euler method and higher-order Runge-Kutta schemes for solving differential equations.

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

Covers the convergence of the method and the importance of adapting time steps for accurate approximations.

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

Covers unconstrained and constrained optimization, optimal control, neural networks, and global optimization methods.

Explores the convergence analysis of the Explicit Runge-Kutta scheme for accurate numerical solutions.

Explores Conjugate Gradient optimization, covering quadratic and nonlinear cases, Wolfe conditions, BFGS, CG algorithms, and matrix symmetry.

Covers hyperbolic problems and the transport equation, emphasizing the importance of weak solutions and the conservative transport equation.

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Covers convergence in induced matrices and advection-diffusion phenomena.

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Covers gradient line search methods and optimization techniques with an emphasis on Wolfe conditions and positive definiteness.

Covers the Runge-Kutta method for approximating solutions of differential equations.

Explains the Runge-Kutta methods, particularly the explicit scheme of order 4 (ERK4), and how to optimize parameters for accuracy.