Lectures

1. Elementary notions on partial differential equations by N. Bedjaoui, France

    1. Classification

    2. Heat equation: separation of variables, Fourier series, Fourier transform

    3. Basic qualitative aspects

    4. Linear transport equation, method of characteristics

    5. Elliptic equations, weak formulation, Lax-Milgram theorem

    6. Exercises about the wave equation

2. Examples of discretization of partial differential equations by J. Correia, Portugal

    1. Euler’s method

    2. Finite difference method

    3. Consistency, stability, convergence, order

    4. Application to the heat equation, boundary conditions

    5. Exercises about the Poisson, transport and wave equations

3. Numerical resolution of linear and nonlinear systems by Y. Mammeri, France

    1. Brief reminder of conditioning, subordinate norms, spectral radius, Gauss and LU decomposition

    2. Iterative methods

    3. Application to the discretization of PDE

    4. Optimization of convex functions, Picard’s method, Newton's methods

    5. Application to the calibration of PDE

4. Practical implementation by M. Pires, Portugal

    1. Reminder of scientific python

    2. Discretization, finite differences, boundary conditions

    3. Numerical solvers

    4. Visualisation

    5. Implementation of the Poisson and heat equations

    6. Exercises about transport and wave equations

Nabil Bedjaoui

University of Picardie

France

Joaquim Correia

University of Évora

Portugal

Youcef Mammeri

University of Picardie

France

Marília Pires

University of Évora

Portugal