High Order Methods: Space Discretisation

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

Numerical Methods: Runge-Kutta Approximation

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

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's definition interval.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

Exam Problems: Nonlinear Equations & ODEs

Covers exam-like problems on nonlinear equations, ODEs, and numerical methods.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Implicit Methods: Retrograde Euler

Covers the retrograde Euler method, an implicit numerical scheme used to solve equations and the concept of convergence order.

Linear Differential Equations: Constant Coefficients and Solution Methods

Covers linear differential equations with constant coefficients and introduces the method of good choice for finding particular solutions.