Métodos Numéricos para Equações Diferenciais Ordinárias

Objectives

To provide theoretical knowledge and skill s on the numerical approximation of ODEs with emphasis in singular problems and convergence acceleration.

Syllabus

Boundary Value and Eigenvalue Problems: Applications in physics; Reducing to integral equations; Collocation methods . Spectral methods; Finite difference and spectral methods for eigenvalue problems. Singular Problems and Asymptotic Methods: Classification of singularities; Asymptotic expansions near regular singularities. Correct statement of the boundary conditions at singularities. Singularly Perturbed Problems: Analytic behavior of solutions; Second order boundary value problems. Convergence Acceleration: Asymptotic error expansions; Richardson extrapolation and its generalizations.

Prerequisites

Elementary numerical analysis, calculus and linear algebra.

Cross Competence Component

The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.

Laboratorial Component

There will be laboratorial classes to help students to carry out the computational works.

Programming And Computing Component

Students must carry out computational works, using programming languages designed for scientific computing, such as Matlab, Mathematica or Python.

Ethical Principles

All members of a group are responsible for the group’s work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.